 So, let us get started. So, you have this will be the last of the torturous lectures as part of this course and what we will do today is to link up some of what we discussed in the first lecture to what has happened in the last lab and the lab that is going to be done this week ok. So, that will be the basic idea of conduct of an experiment you have done fair bit of electronics you have gotten in introduced to a few things that you see commonly in all data acquisition systems you have spoken about it you have a sensor producing analog voltage goes to an ADC process by a microcontroller maybe a DAC later on that is the structure of all DAC systems data acquisition systems. So, you have gotten exposed to that you also did a couple of rounds of calibration ok the basic idea of calibration why is it important because all the numbers that you generate through an experiment has to do with some meaning that you derived out of those numbers and that meaning is derived prior to you conducting the experiment ok that is done through the process of calibration. So, you got introduced to that little bit about the notion of accuracy precision not delving too much into it. The last experiment was something that we will discuss now I mean the lot of things happened during the course of that experiment which you may not have had the opportunity to pay adequate attention to. So, we will discuss that now as well as this week's experiment ok. These two things we will discuss now and tie it with physics which is ultimately what experimentation is all about ok. So, we will focus on the idea of validating a hypothesis or a model and experimental procedure is important to do this systematically confidently repeatably etcetera. So, in the first lecture this slide was put up why do we need to experiment you are all going to be part of the scientific community and you need to be able to validate if a certain hypothesis that is posed to you is valid or invalid and that is the basic idea of why you need to do experiments. So, we will come back to that idea and how it relates to the two things that you have done in the that one you have already done one you are going to do now ok. So, we will discuss the beam experiment ok. So, you may not have been aware because of your preoccupation in the actual conduct of the experiment some numbers being thrown around procedure is not clear that is not happening this voltage is not coming out etcetera, but there were several hypotheses that could have been validated or invalidated during the course of the experiment ok. So, was there a hypothesis that you were aware that you were validating or invalidating. So, those people who think they have some idea of what hypothesis or what you can come up with anything you want pertaining to the last week's experiment that you think was validated or invalidated ok one year anybody else who thinks no idea of what hypothesis was being validated ok. First let me remind you what the experiment was. So, you had a beam. So, this beam was screwed at one end. So, basically clamped and you had strain gauges mounted at this end of the beam ok. So, these are the strain gauges. So, these strain gauges as the name suggests are used to measure strain of course, strain meaning as far as you are concerned you can think of it as elongation or contraction ok. So, when you are bending something this part elongates ok. So, you take a scale and bend it on this side holding this constant you will you will see that you can imagine that the top part of the scale will elongate and the bottom part of the scale will contract ok. So, the strain gauge is used to measure these sort of small elongations and contractions. So, how does it work? It works through the principle of changing resistance. So, when a strain is applied to certain certain materials their resistance changes ok. And this is known a priori to the people who are manufacturing strain gauges and there they have already calibrated how much the resistance changes for a certain elongation or contraction of the strain gauge. This is already been done by the manufacturer of the strain gauge ok. So, those strain gauges were mounted here and were used as part of a bridge network. You know what a Wheatstone's bridge is you must have solved these problems. So, suppose you apply a voltage across this sort of a bridge network network of resistors you can compute the unbalanced voltage here given this voltage and the ratio of the resistances. This you must have done it is straightforward application of your principle of charge conservation that Kirchhoff's current law and the voltage law ok. So, what was done was these strain gauges were used as part of as the arms of your bridge network because of which you got an unbalanced voltage which was amplified using op-amp circuitry that was displayed on your oscilloscope or you measured it using a multimeter ok. So, what you effectively measured here was strain that is the amount of elongation of the top surface when you put a weight here. So, you put a weight here and the because of the weight this thing deflects and that deflection really creates an elongation here and you are able to map the elongation that you have here to the weight that you have here. So, you put different amounts of weights you saw different elongations and different voltages that you saw as the imbalance here is it clear what was done last time around that was the first part of the experiment then you. So, you did this for several weights and you did a plot of deflection as recorded by the strain gauge to the weight that was applied ok. So, this was related to the voltage through the calibration table or the other way round through the calibration table. So, you measured voltage and went to deflection using a calibration table is it clear everybody what happened last time around then you did something interesting I do not know how many of you understood what was happening after that some k computation and some mass computation and some funny things happening ok. So, after this what you did was you came up with a chart where you computed a quantity indicative of stiffness ok. So, how that quantity got computed was that you took the weight that was applied divided by some measure of the deflection ok. So, that deflection was measured here using your screw gauge. So, the deflection was measured there. So, weight divided by deflection is Newton per meter is the units of that quantity what is that quantity signified did anybody think about that of what it is spring constant of what right may be right man right man spring constant of what of the beam what do you mean spring constant of the beam explain what do you mean by the term spring constant of the beam. Tell me do you understand my question whoever has the mic now? No sir. Ok. Do you remember what I am talking about? Yes sir. Ah you were there for the last experiment or you did the last experiment or no? Yes sir. You did ok. So, you computed a quantity k yeah is the ratio of weight over deflection as measured by the screw gauge. Yeah. I want you to tell me what this means. This is same as the k that we get in finding out g sir. Finding out. Like g equals to 1 by 2 pi times under root k by m. G. Gravity the fundamental the natural frequency of the what I am asking a simple question what is this w by delta why was it computed? To find out k. What is k? k is nothing but the under root k by m is nothing but the fundamental frequency of the material. I am asking you what is k then we can go under root k by m, but you know under root k by m is something. Yeah. Ok. Why? You are comfortable with that I do not know what is k, but under root k by m is something. What is k? Sir that is spring constant for the vertical displacement of the beam. It is because because it has been used lot of times before in the context of spring constant you are saying spring constant. What spring? What springiness are you talking about? By the way this is not an easy question to answer. So, do not I do not think most of you will get it even after we have a discussion. So, the point of the discussion is for you to get thinking about it. What spring? I do not see a spring I see some beam there. Sir the vertical motion of the beam makes it behave as some spring the oscillations. So, it is same as the spring constant if we put a spring in place of it. So, it would be same as the spring constant. What your line of reasoning is alright, but if we put a spring how? Is my spring going to be like this and my weight sitting here and it going like this? Sir it would be elasticity of the beam. Yeah it is related to the elasticity of the beam, but you are talking about a vertical spring right some mass and a vertical spring. Is this what you are talking about? Sir if we equate the frequencies, sir I am guessing if we equate the frequency of the vertical oscillation of this beam. No, no, no, before we equate the frequency I am asking you what does that k represent? That is elasticity of the beam I told you. Okay we will get two more comment or one guy who is put up there and basically the material behave different differently in different directions. So, the elasticity in the vertical direction is basically what is k? Okay both these answers put together pretty reasonable, but we will get some more here. So, the main thing I want to get out here is this k is actually a human contraption right which can be given lots of interpretations okay. Inherent in this k in the competition of this k is a model, a model is and something that human beings construct to describe a physical situation okay. Models are very important to engineering because we are not able to describe or understand the physical situation in totality as it exists. So, what we do is that we solve some toy problems okay and assume that those toy problems or the setting of the toy problem applies to different situations okay. What I am discussing here is philosophically very important, do not dismiss it, it is fundamental to engineering and science okay. So, all these problems that you do in your in different courses your whatever JEE preparation that this these are all toy problems I mean have you ever seen anything like this in your life spring and something hanging like this probably not very few people would have actually seen something like this and some oscillation happening or some other set of pulleys and moving around here and there very rarely you see all of these things why are you doing all this one is to clear some exam that is not that is not the real answer the real answer is that by solving these toy problems with a whole set of assumptions assuming Newton was right blah blah blah you come up with a certain solution of the toy problem right and then you assume that the same setting sort of thing applies in reality okay that assumption is critical and you assume that that solution here will give you a reasonable estimate of what is happening in reality do you understand the process you solve toy problem because that is all you know how to solve you can draw something on paper and compute something and feel very important intelligent okay. Then you relate that toy problem to a physical situation how you relate that is is the essence of engineering it is not the ability to solve those toy problems because eventually people will get to know how to solve the toy problems but the good engineers are the ones who are able to relate some types of toy problems to some physical situations or the same sort of toy problems to a wide variety of physical situations that is where the engineering charm is okay so what you ended up doing last time hopefully you two are representative of a reasonable number of people sitting out there is that you assumed that this toy problem applies to the situation that you are dealing with that is if you solve this toy problem for some K and that K coming out of that experiment vertical spring and a mass moving around okay what mass are you talking about here this guy saying mass that is kept on it so the masses the mass there's some effective mass of the beam that the spring to speak a little louder there's an effective mass that of the beam as seen by the spring which is different from the mass of the beam right so there is something called effective mass now where did that effective mass come from okay for this effective mass to be valid you need to go through a process of of assuming some mass and computing the mass which will give you the through which you can say that the frequency that is measured is the same as the frequency that comes out of this this toy problem you understand that mass is called the effective mass so inherent in what you did you do you may not know what you did which is the case for most people through their lives is the assumption that there is a model used to describe this and we are trying to equate what happens or the predictions of the model against what is that what is actually measured okay so the hypothesis that was tested was this that a spring mass model of the of the form that you see or we just saw the spring mass model is useful to estimate the fundamental frequency of vibration transfer vibration of the beam that is the hypothesis that we tested so suppose somebody came and told you you use a spring mass model this this problem you need you know how to solve in estimating the frequency of free vibration and you this problem applies to the beam suppose somebody came and told you that how does it apply to the beam you compute the mass of the beam put it here as a mass of the beam and compute this quantity by measuring displacement for different values of weights you put on it and compute that k I mean this is a weird procedure do you realize it's a weird procedure it's not something that you would just come up with so how many people is this obvious that this is the way to get k and what what sits here has to be the mass of the beam I don't think too many too many people will be comfortable saying that okay this k if you compute this way and this mb with mass of the beam given all volume and density etc if you stick in here and compute the free vibration frequency you will get something close to what happens in the beam that is the hypothesis that is that is not a true statement it is a statement which you need to validate or invalidate by conducting an experiment okay so do you understand what hypothesis got validated or invalidated I think what you would have gotten is some number which is in the same ballpark as what what was estimated but not really the same thing maybe half or twice or something like that you would have got right I think this was 9 hertz and that was some 18 hertz or something some some such number okay so what the mass spring model with the assumption that the k comes from this p over delta sort of thing was approximately 9 hertz I'm told and the experimentally measured thing was 18 hertz I mean you looked at the oscilloscope right but the important point is not whether to say I 9 hertz okay 18 hertz okay what do you do with it the point is you could estimate that this will be in the order of a few tens of hertz just by by taking a piece of paper and conducting an experiment without actually making it vibrate so that you were able to do because you had an inherent model in your brain and that model was what we described in the sheet of paper okay so a lot of things that are happening in in every experiment if you really delve into the questions that are going behind it you will see that it's not very easy to come up with comfortable answers that you are going to be satisfied with okay so so think about it I'm not asking you to accept what I've said as these are some weird things I just some k and some mb I mean you can come up probably with a better model to describe it okay but nevertheless even something as simple as this seem to seem to give you some some reasonable numbers okay so that was the point of the last experiment that you can actually construct a model and predict something so these these problems these toy problems are not a waste they're not there only for you to clear exams okay now we are going to do a toy problem we're going to understand this toy problem so how many you so in your you did physics one was any mechanics taught to you physics one no only electromagnetism okay so what we are going to do here is some basic Newtonian mechanics it's not not difficult at all so we are going to describe the motion of this guy this type so understand the important thing to understand is this is a toy in front of you this is not reality okay you should not go away from your bachelor's program thinking that this is reality this is this this is not reality these are some some things that you have concocted okay so you drop free body diagram of this assuming some some extension of the spring spring is going to pull it back kx okay and that is responsible for the acceleration in a direction opposite the pulling of the spring so the acceleration ma or this is x double dot is negative kx okay so that's this equation is again a human construct Newton told you this and you believe it this is not reality okay but we are not dealing with reality now we are dealing with this this space which is unreal space so you have this unreal space which is behaving like this okay free vibration when no external force is applied now we tell for those of you who know how to analyze linear differential equations you must have done a course in od is yes maths to one part of it was od is the other linear algebra they're closely linked to each other okay so how many of you can confidently analyze the behavior of this od raise your hands nicely confidently analyze so those who are not confident I will ask you do you understand the question first of all how many of you can confidently analyze this od analyze you know what analysis is how does this this beast behave what sort of x will satisfy this equation okay those sort of questions okay so what sort of x will satisfy this equation okay so the what sort of x will satisfy this anybody satisfy this equation they're dealing with okay same sort of equation appears if you have an lc circuit lc oscillator any volunteers for what sort of equation what sort of x will satisfy this equation do you understand the question what sort of x satisfies this equation means if you plug in that x and you do mx double dot plus kx you will get zero that is what I'm asking uh x equal to sine omega x satisfies all cos omega x x equal to sine omega x equal to a sine omega t plus b sine b cos omega t because omega t is same as sine we just you guys are like children here crazy fellows okay so uh this is a candidate so the reason why this works do you know the reason why it works or you just know that it works in this case acceleration is proportional to x and at mean position the acceleration is zero so for simple harmonic motion the object has tendency to move towards the mean position but where from the object has tendency to move to the mean position that's fine but how do you know that the object moves with this sine sine omega feature that's the question why should this structure work I can have I can have a motion where I always pull back with the constant force when I'm away I pull back with the constant force and this side I'm also pulling back with the constant force so I come back to the mean position but the answer to that situation will not be the same this is your 11th standard 12th standard through je stuff you're giving me all parroting all that I want something more than that so I'm spending a lot of time here because it's it's important for this experiment also it's important that you understand this yeah sir maybe because uh it's double differential is also sine omega t yeah so the the structure of the equation is the is the important part that certain functions when double differentiated will give you the same function but scaled by a different quantity okay so in this case if you have sine omega t as your function do a double derivative of that you get some scaled version of sine omega t okay and that seems to work seems to fit this this bill because mx double dot is a scaled version of x okay so that's the reason this this works okay so this sort of a function which when put through a system does not change in its character but only changes in in its scaling is called an eigen function very similar to the notion of an eigenvalue okay you have a matrix you hit it with a vector what you get out if you get the same vector but scaled by a different quantity that sort of a vector is called an eigen vector so the equivalent of the eigen vector for linear differential equations is your exponentials but in this case it's a complex exponential okay so the reason why this works is because of the specific structure of the equation okay and this omega that we are talking about happens to be your root of k by m okay you can convince yourself it's not difficult to convince yourself if you take x is a sine omega t and just plug this in okay so you get m a omega square sine omega t plus a sine omega t k equal to 0 so then you you find out that omega has to be root of k by m it cannot be any omega but a specific omega okay so this is the reason why or this is how this toy problem behaves in our own minds we have created a toy problem applied Newton to it we have solved that differential equation so applied some mathematics to it interpreted it in some way but this is all on paper okay so now we stick this stick this guy together with this root of k by m I put this k and mb and compute this quantity root of k by m okay then there is some radiance per second hertz and all of that so that's that's not important okay so this quantity is computed through by assuming that this model of of transverse vibration is valid okay so that computed quantity is compared with reality that's what you ended up doing and you found out that they were different but they were in the same ballpark okay so this was what was done in the previous experiment so what are we going to do in this experiment we were going to obviously test another hypothesis or validate or invalidate another hypothesis okay so you've you've been exposed to this so many times over you accept it as granted okay so the hypothesis is a hypothesis that's not going to stun you okay it's a acceleration due to gravity is approximately 10 meter per second square close to the surface of the earth okay now there are a lot of things that that go into making a statement like this first of all why should there be something called an acceleration due to gravity which is a constant first of all okay there is a lot of questions that you can ask but suppose you assume Galileo was right Newton was right etc and then you said that there is a quantity called the acceleration due to gravity which makes sense close to the surface of the earth and I want to compute that quantity or I want to estimate what that quantity is the claim here is that quantity is approximately equal to 10 meter per second square so this is the hypothesis you're going to end up testing or validating so what there is the result of your procedure will be that yes I agree it is approximately 10 meter per second square or I disagree it's approximately 10 meters per second square because of this reasons okay so how do we test a hypothesis like this ideas are very simple but actually executing it and coming up with a number is not so simple okay so we'll just step through it so how does one validate a hypothesis like this any ideas okay so somebody here says you put a spring mass oscillator like this and then what what do you do so you get elongation how do you know spring constant yeah so frequencies and this thing will work yeah yeah so one you must have done a leaven standard experiment or it is part of your syllabus didn't do it at all some bob is moving around like this okay sitting at the stopwatch long bob how many of you did this experiment actually did it don't lie how many of you actually did this experiment okay I'm not asking whether it was part of your physics lab or not that's a different question that's like asking how many of you did ic211 all of you right so how many of you actually did the experiment with a stopwatch okay so one way to do it is with a pendulum okay so now time to find out if you understand the physics of the pendulum so here so how does one validate this hypothesis you have to actually physically construct a pendulum that we are not going to ask you to physically construct it it's not that difficult but you need some elements for that also once you construct a pendulum what we are going to do is we are going to measure the time period of the pendulum for some displacement from its main position equilibrium position let it go it keeps doing this and you measure the time period the same sort of experiment that you did in your leaven standard but done a little better okay the little better comes from measuring the time accurately so the time is going to be measured using a microcontroller that's the only conceptually you're not doing something different it's like a stopwatch but it's done better you're not waiting for it to so when you if you have ever done the experiment in the lab in the physics lab it's not very easy to find out when it actually reached zero velocity you just assume a zero velocity it has reached or when it is actually reaching the center and then there is a time lag between when you decide it has reached and when you actually press okay all that is happening so you're measuring time a little better using a microcontroller but the principle remains the same the third part of it just by measuring time so what you're measuring some time you should be able to correlate the time to this quantity called acceleration due to gravity okay that correlation requires what it requires you to construct some model on paper and understand the behavior of the model you have constructed okay so that's the reason why you need to know how to construct models and understand the behavior of your own models okay it's not it's not some exam exam related stuff so if you actually want to validate this hypothesis which has been assumed to be true all the way along okay throughout your life you will assume it to be true okay so the model you will construct is this so this looks this is an easier model to construct by the way than the previous previous labs experiment because there is a one to one correlation between the way this looks on paper and the way actually the pendulum is going to look okay so we are going to deal with something like that this guy displaced version another displaced version this is how we picture a pendulum also okay so this model is easier to construct from a physical point of view than the k and mb etc we used in the last experiment okay so now i'm going to get a bakra who's going to tell me the physics of this model we can assume a small theta displacement you said you're going to do it yeah sorry sorry assume small theta displacement and then we can write down the equations equations so there will be an mg force acting downwards okay tension along the string along the string string and then we can take the components of the mg perpendicular to the string and along the string mg sign theta and mg cos theta okay great so far so good so now the mg sine theta will be providing the torque torque providing the torque torque about this point here you're going to talk about yes okay so mg sine theta into l will be equal to i alpha and i is ml square so now we'll approximate theta as theta is small sine theta is approximately what is alpha alpha is the angular acceleration okay what happens to t and mg cos theta pardon me sir how are t and mg cos theta related sir mg cos theta will be equal to t how many of you agree how many of you agree t will be equal to mg cosine theta raise your hands here you should guys should not have cleared j e t will be equal to mg cosine theta only if it's not accelerating is it accelerating or not yes no it's accelerate centripetal acceleration so t minus mg cos theta will be equal to m v square by r okay fine so how many of you are happy with this equation how many of you are happy with this equation so those others i assume are either unhappy or they don't care who is unhappy nobody's unhappy also rest don't care i'll don't lot of don't cares what is alpha angular acceleration tell me what is alpha so it's angular acceleration you have to speak into the mica it's angular acceleration how is it related to theta is it related to theta okay yes or no it is related to theta it is related to theta yes how minus omega square theta minus omega square theta minus omega square theta what omega angular velocity why is it omega square theta minus omega square theta what do you mean by acceleration how is acceleration related to displacement i'm not going to let you go when you can feel as bad as you want how is acceleration related to displacement theta is your angular displacement and alpha is your angular acceleration how is acceleration related to displacement how is acceleration related to velocity is the rate of change of velocity acceleration is rate of change of velocity okay so now how is acceleration related to to displacement. How is velocity related to displacement? The rate at which. Come on. Velocity is the rate at which displacement takes place. Okay, then how is acceleration related to displacement? The double derivative of. Double derivative of displacement. What do you mean by omega square theta? I mean you mean these, you are not thinking at all. This is somewhat related to double derivative. Actually, this is a symptom of what happens over here. Okay, after you clear your exam. Not very many people really understand stuff. Okay, whether you like it or not. So, when confronted, what do you really understand? You come croppers. Just because you can solve some problems and get some marks, doesn't mean anything. Okay? Okay, so how many of you are happy with this equation? This equation. This equation is correct to describe the physics of the situation. How many of you say this? How many of you don't say this? Or how many of you say it is incorrect? Anybody else? Anything else wrong with this? Some minus sign. Yeah, that's similar to what happened in the previous case. You displace it and the acceleration which tries to restore it is in the opposite direction of the displacement. Okay, so you acknowledge that by saying if the displacement is considered to be positive in certain direction, your acceleration is in the other way. Okay, you have a minus sign there. So, what is called the governing differential equation. Okay, this, remember this equation comes from a human construct which is a model to describe the pendulum. This is not the pendulum. This is not the pendulum. Okay? This is a model of the pendulum. And then you apply some equations making some assumptions. So, the governing differential equation is this. So, we are going to find a theta which solves this. Okay, for somebody mentioned for small theta, the governing differential equation behaves like this. We make the approximation that sin theta is approximately equal to theta for small theta. Okay? So, if your displacements are small, then you can assume that this governing equation describes the behavior of the pendulum. That's what, that's the statement we are making by making a, so this is very similar to what you saw. This is your mass. This is your spring. And if you find an a sin omega t which satisfies this, it's the same thing as the mx double dot plus kx equal to 0. It's the same equation. There's no difference at all. So, what you will get is root of g by l is your frequency. Now, this is a prediction. This prediction you will assume is right. You will assume that this prediction is correct. And you will find the value of g such that the prediction matches reality. This is different from what you did the last time around. The last time around, you did not even assume the prediction was right. Okay? You did not assume the model was correct. Here you will assume that the model is correct and you will match what the prediction comes from the model or we will assume that what comes from the model is equal to what happens in reality, then estimate g. Okay? So, this is your frequency and obviously your time period will be related to the inverse of this. And if you're talking about, so this is related to your time period. So, if you're able to measure time period in reality and you assume that this model is correct, then you can get an estimate of g. Okay? So, that was the third bit of what you need to do to be able to get there. You will have to assume Newtonian physics is correct in this situation. Only then you will be able to get the estimate of the parameter. Okay? Now, you don't even have to assume the Newtonian physics is correct if you can construct a lot of different pendulums. You can construct a lot of different pendulums, look at the ratios of the t1 to t2 for a lot of different pendulums and then from there you may arrive at the conclusion that there is a quantity g which seems to remain constant. Okay? That's a different set of, that's a different experiment. But that is not our experiment. Okay? So, now we will spend some time on understanding how is it that you will get the time period? Okay? So, you will use a microcontroller like I told you. So, you will have a pendulum, it's not exactly how we spoke about. So, this pendulum is going to go into the paper and out of it. Understand? So, side view is going to look like this. Now, we are going to put a source of light here and a detector here. So, this guy is a light source. So, every time this pendulum bob obstructs the light, the detector is going to see a change. Okay? You are going to capture the time of that change by connecting schematically. This is connected to a pin of the microcontroller. On your board, you will see the top right corner has a few bit IOs. Okay? So, one of those, it is going to get connected to. So, obviously, it is not a straight connection like this. There is some signal conditioning electronics in between. But basically, every time the light source is obstructed, the voltage level of what is getting connected here is going to change from high to low. It has been designed that way. So, your job is to estimate the times when it goes from high to low. So, now there are some specifics. So, this is not a real point mass. It has a physical dimension. So, if it is moving to your right, to your right, then you will see this edge first. Okay? The obstruction will begin. Okay? So, you will go from high to low, then again low to high when the obstruction ends. So, you will see some behavior which is like this ideally, but it won't really be like this. It will be like this. Very close to the change, you will see some funny behavior. If you actually measure it in the oscilloscope. So, your job is to get this T1, T2, which will tell you at what time the bob pass this way. And at the same location, you measure the time it comes back. So, you will have T3 and T4. Based on this, you can estimate the time period of your pendulum. Okay? If you know T1, T2, T3, T4 in seconds, you can, I am sure all of you will be able to come up with some estimate for the time period. So, that's, that's pretty much what you are going to end up doing except that the job of doing that will be through the timer module of the microcontroller. So, you have been exposed to the timer module, struggled with it in one of the previous experiments. The timer module as I mentioned to you has a counter which gets incremented at an integral d multiple of the bus frequency or the clock frequency. Okay? And your job in the timer module is to understand what the clock frequency is, what integral d multiple you are using for your timer counter and how many counts of that integral d multiple have elapsed. That will give you an idea of time. Okay? So, what you need is actually the difference between these two things, the difference between these two things and the difference between these two things, not the absolute versions. Okay? That's what you really need. So, the timer module, so, two things for you to remember. So, I will look at the programmer a little bit. I am not going to construct the program for you. The structure of the program will look like this. Like we have already discussed all of microcontroller programming where you are dealing with physical signals boils down to setting register values appropriately. There is nothing more to it, nothing less. So, you have to understand the different modules or the different resources offered by the microcontroller. Understand what registers to be set to what values. So, you will use the timer module. Okay? We will also use serial port interface where data that you obtain has to be communicated somewhere. You will do something a little different from the ideal situation. So, ideally some behavior like this is going to be seen. But since you have some noise around here, every time you see a change, you will wait for some time before recording because a change has a change actually happened. Okay? Because you will see noise before and after. So, you will have to put in a delay. Small delay. It should not be too large and otherwise your estimate of time is also corrupted. Okay? So, you will have to use the serial port interface, the timer module, introduce delay every time you see voltage change on a pin. So, this is your algorithm pretty much. You will have to worry about one more thing about overflows because the timer counter can overflow. So, you will have to worry about how to handle overflows. Okay? And handle overflow. So, this is what your program will end up doing. Okay? Is it clear overall what the program will end up doing? The program will use the timer module to get estimates of time. It will introduce a delay every time there is a change. So, how do you know that there is a change? You have to keep looking at something. Okay? So, that activity can be done in a variety of ways. One way of doing it is polling. Keep asking. Have you changed? Have you changed? Have you changed? Have you changed? Okay? That's the activity you will use to find out if there has been a change. And every time there is a change, you will wait for a small period of time and then record the time as given by the timer counter. Keep repeating this procedure as it's going up and down. Taking care of overflows. Overflows means timer counter goes all the way and comes back. For you to be able to do this, we will give you a structure of a rough structure of the program and then you can set register values and play with it. So, obviously, there are a lot of assumptions that go into this being correct. Of course, you can measure time much more accurately than you do with a stopwatch. But again, the estimate of time period that you get will be subject to the assumptions that you have made of things working. Okay? I mean, that actually when the fall happens, that is when the thing passes all those assumptions are there. But the assumptions are more reasonable than your stopwatch. Okay? So, that's how you will get an estimate of your time period. With that, you will construct. You will assume that the physics of it is the way we described it. Get an estimate of what the time period should be. Compare it with reality. Get estimate of G. Is it clear? What you will end up doing? The experiment itself is not very complicated. It is actually a very simple experiment. The way it is constructed is not difficult to put together a pendulum, not difficult to put together light source connected to a microcontroller etc. But the philosophy of what we did is not different from any other experiment. First, you construct a hypothesis. Construct a procedure which by which you can get something about the hypothesis. Most of the time, if you are estimating parameters like we are estimating the value of G, you will have to assume some physics associated with with the situation. In this case, the physics comes from Newton. Okay? It may come from it may come from other guys, Maxwell or whoever it is. And then you estimate the parameter. The process remains identical. So, you have a measurement procedure by which you compute some number based on which you compute the value of the parameter. This is how you go about estimating every parameter. What the experimental procedure is? What measurement systems you use? How you interface it with electronic circuitry? Those will change from experiment to experiment. But the basic idea of how to conduct the experiment remains the same. Okay? Also, what you have learned in this course? The basic structure of modern-day data acquisition systems will also remain the same probably until the next 10-20 years before there is a drastic change in the technology. So, that is also a useful thing to carry forward. Okay? So, at the end of it all, if you have a reasonable flavor for the following. Okay? Reasonable flavor for what goes into a data acquisition system. Okay? So, if you have a reasonable flavor for what a modern-day data acquisition system looks like, what are the elements of it? ADC is microcontrollers. Reasonable flavor of typical electronic prototyping devices, multimeters, oscilloscopes, right? Some familiarity with these things. This is the absolute basic necessity that the course should have taught you or the absolute basic stuff the course should have taught you. On top of this, if you are able to appreciate some of the ideas behind measurement systems, calibration, accuracy, repeatability, reproducibility, precision. And on top of this, if you understand the context of performing experiments, role played by experiments to validate hypothesis, role played by models in the process of validating hypothesis, you've been able to put all that together, then you have actually understood the flavor of the course. Okay? So, hopefully we have been able to give you a gist of all this. The idea is not to make you exactly be able to measure something in a specific situation, but give you the necessary background to ask the right questions to do that. Okay? So, that was the intent of the course. If this has overall been, I mean with different degrees of certainty for different people, then we would have done a reasonable job of introducing this course to you. If that has not happened, either we have not done a good job of your, you have not done a good job of assimilating it or both. Okay? So, what was this course about? Hopefully it is reasonably clear after this, after this lecture. If you have any questions on philosophical aspects as well as some detail for the experiment that you are going to conduct, we have four or five minutes. Any questions? You don't have to feel so jittery. You can sit here for a little while longer. It's not direct. So, the question is, instead of taking the sensors output directly into the microcontroller, why don't you do some signal conditioning such as noise cancelling? That's already been done for you. So, you are not going to design that noise cancelling circuitry. It's already been done. Secondly, because a large part of the way the course is conducted and the way it is delivered, three people sitting in front of a, you know, on a workstation, two people sitting on a workstation, does not make it possible for you to differentiate between the person who's doing the experiment, not doing the experiment during the course of the experiment. Okay? So, the N-SEM quiz, though it will not have the biggest weight across the mark spectrum, will decide your grade basically. Okay? Because that is going to differentiate who has understood something, who has not understood something. Because, more or less, otherwise, many of you have shown up for the experiments and done something. Okay? So, the idea is not to say that, oh, this guy is great and that guy is not great. But the idea is for us to know how many of you have had a reasonable understanding of what has happened. Okay? Trust me, you're not going to be bothered about this grade ever in your life. It's going to appear very important right now. It doesn't matter. Okay? So, the spirit of the exam is for us to understand and for you to show that you have understood something. And in the middle of all this, you have some grade and some CGPA and all that being computed. Any other questions? Logistics? Okay. So, we're done with the course.