 Hello everyone, welcome to this session. I am Priyanka Bansori and today we are going to study about analogous system in that force current analogy. These are the learning outcomes of this video lecture. At the end of this session students will be able to explain force current analogy for translational system and explain torque current analogy for rotational system. These are the contents of this video lecture. Before moving towards force current analogy pause this video for few seconds and you have to recall analogous system at its types. Now pause the video. So first upon analogy means a comparison between one thing and the another and we are having two different physical systems with the same mathematical model then they will be called as analogous system. So here in between electrical and mechanical systems there exists a fixed analogy and exists a similarity between the equilibrium equations. So it has two types. So one is the force voltage analogy and the another is force current analogy. Now in this video lecture we are going to discuss about force current analogy to convert mechanical system into the electrical system. So there are two types mechanical and electrical. So in mechanical system there is an input and output. So input is force and the output is in terms of velocity or in terms of displacement. So coming to electrical system. So here input is current source in force current analogy and output is voltage across the element. In previous video lecture that is in force voltage analogy input is voltage source and the output is current flowing through the element. So you have to remember one thing the elements which are in series in force voltage analogy get connected in parallel in force current analogous network and which are connected in parallel in force voltage analogy get connected in series in force current analogous network. Now consider simple mechanical system as shown in figure 1. The mechanical translation system having three elements spring mass and the damper or friction due to applied force mass m will displace by an amount x in the direction of force as shown in figure as we have discussed in the previous video lecture. So according to Newton's law of motion the equation is f of t is equal to m into a plus b into v plus k into x of t. Here the output is in form of velocity or displacement. Therefore f of t is equal to m d square x of t by dt square plus b dx of t by dt plus kx of t. Now taking the Laplace of above equation. So the equation becomes f of s is equal to m s square x of s plus b s x of s plus k into x of s. So this is the equilibrium equation for the given translational mechanical system. Now we will see force current analogy for the translation system. Now we will try to derive analogous electrical network. So consider an electric network as shown in figure 2. Here R, L and C are connected in parallel and in this method to the force in mechanical system current is assumed to be analogous well. Means what? The force f is analogous to current i in force current analogy. So we will try derive other analogous terms. According to Kirchhoff's law of current the equation can be written as i is equal to iL plus iR plus ic. So the equation terms of voltage i is equal to 1 by L integration of v dt plus v by R plus C into dv by dt. Now taking the Laplace of above equation. So the equation becomes i of s is equal to v of s by iSL plus v of s by R plus sc v of s. But to get this equation in the similar form as that of f of s then only we will compare the equations for analogous network. So we will use voltage is rate of change of flux with respect to time. So v of t is equal to d phi by dt. Phi is the flux. Now taking the Laplace then equation becomes v of s is equal to s phi of s. Now put this value in the above equation and the equation becomes i of s is equal to 1 by L phi of s plus 1 by R s phi of s plus C s square phi of s. Now the equation of i of s and f of s is in the same form. Comparing equations for f of s and i of s from above equations we can say that capacitance C is analogous to mass m then reciprocal of resistance that is 1 by R is analogous to friction constant B and reciprocal of inductance is analogous to spring constant K. Now compare translation mechanical and electrical system here we compare the analogous elements in force current analogy. So force force f is analogous to current i then mass m is analogous to capacitance C and the friction constant B is analogous to reciprocal of resistance. Then spring constant K is analogous to reciprocal of inductance. Displacement x is analogous to flux phi and finally velocity v that is dx by dt is analogous to the voltage is equal to d phi by dt. Now let us see the mechanical rotational system in the figure this is the motion about fixed axis in such systems the force gets replaced by a moment about the fixed axis that is called the torque already we discussed in the previous lecture. So according to Newton's law of motion the equation of rotational system eats here the force is replaced by torque. So the equation becomes T of t is equal to J alpha plus B omega plus K theta of t J is the inertia and then put the value of alpha and omega into the above equation then the equation becomes T of t is equal to J d square theta of t by dt square plus B d theta of t by dt plus K theta of t. Now taking the Laplace of above equation T of s is equal to J s square theta of s plus B s theta of s plus K theta of s. So this is the equilibrium equation of rotational system. Now let us see the torque current analogy for rotational mechanical system. Here the force is replaced by torque so it is called torque current analogy. As discussed in previous lecture force voltage analogy for rotational system is also called torque voltage analogy for the rotational system. Now again compare the equations of T of s and I of s. So from the above equation it is clear that capacitance C is analogous to inertia J then reciprocal of resistance is analogous to torsional friction constant and the reciprocal of inductance is analogous to spring constant K. Now finally we compare the analogous elements of rotational system with electrical system. So first torque T is analogous to current I. Then inertia J is analogous to capacitance C. B is analogous to reciprocal of resistance. Then torsional spring constant K is analogous to reciprocal of inductance. Angular displacement that is theta is analogous to flux that is phi. Angular velocity alpha is analogous to the voltage V. So in this video lecture we have discussed the force current analogy for the translational system as well as torque current analogy for rotational system. Let us see the procedure to solve problems on analogous system. There are total seven steps so we see one by one. So step one identify all the displacement due to applied force. So it means total number of nodes is equal to total number of masses is equal to total number of displacement. Step two is draw the equivalent mechanical system based on node basis that is force voltage analogy means the elements under the same displacement will get connected in parallel under that node and each displacement is represented by separate node. Then step three is write the equilibrium equations or system equation at each node algebraic sum of the all forces acting at that node in zero or input force is equal to output force. Then step four is in force voltage analogy use equivalent analogy terms as we have seen earlier. Then step five is simulate the method using force voltage analogy. Then step six similarly in force current analogy use the equivalent analogy terms and the last step simulate the method using force current analogy. So with the help of these steps we have to represent the even mechanical system into the electrical system. These are the references of this video lecture. Thank you.