 Hello everyone, welcome to this session. I am Priyanka Bansoday and today I am going to explain example based on force voltage and force current analogy. These are the learning outcomes of this video lecture. At the end of this session students will be able to evaluate the equivalent system and equilibrium equations then represent a given mechanical system into the electrical system. These are the contents of this video lecture. Before moving towards to solve the example pause this video for few seconds and you have to recall steps for conversion of mechanical to electrical system. Now pause the video and seven steps we will see one by one. So, step one is identify all the displacements due to applied force. So, find out the total number of mass and the displacements. Then step two draw the equivalent mechanical system based on the node basis and write down the equilibrium equations. Then step four in force voltage analogy use the equivalent analogy terms and the step five simulate the method using force voltage analogy. Then step six is in force current analogy use the equivalent analogy terms and similarly simulate the method using force current analogy. Now we will see the example for this physical system draw its equivalent system and write the equilibrium equation. Hence draw its electrical analog system based on force voltage and the force current analogy. So here force F is applied on mass M2 and because of that force displacement is occurred. So, here displacement X2 to mass M2 and the displacement X1 to mass M1 occurred. Here force is getting distributed in all elements and distribution of force along with mass is always with respect to reference. So here the mass M1 and 2 is connected between the node and the reference. So for mathematical modeling every mass is connected between the node and the reference. So M2 is connected between the node X2 and the reference and mass M1 is connected between the reference and the node X1. So reference is also shown in the figure. So first we have to go through the steps. So step one is number of displacement is equal to number of masses is equal to number of nodes. So here there are the two masses. So there are the two nodes. Then step two draw the equivalent mechanical system. So for that purpose here X1 and X2 are the nodes and M1 is connected between X1 and the reference. So M2 is connected between the X2 and the reference and you can see in the mechanical figure that is in the left hand side figure K2 is the spring constant that is connected between the node X1 and X2. So in the equivalent system K2 is connected between the X1 and X2 and similarly K1 and B is the damper are connected between the reference and the node X1 and the force F is connected in the direction of displacement. Step three is write equilibrium equations at node X1. Similarly at a node X2 we have to write down the equation input force is equal to output force. So here X1 and X2 are the nodes. So for node X1 input force is F and the output force is due to mass M1, B, K1 and due to K2 and for node X2 input force is due to K2 and the output force is due to mass M2. So according to that you have to write down the equation but whenever you have to write down the equation in terms of K2 at that time node X1 as well as node X2 is also considered. So from the figure we can write down the equation. So F of t is equal to M1 d square X1 by dt square plus B the X1 by dt plus K1 X1 plus K2 in bracket X1 minus X2 taking the Laplace of above equation and the equation becomes F of s is equal to M1 s square X1 of s plus B into s X1 of s plus K1 X1 of s plus K2 in bracket X1 of s minus X2 of s. So this is equation 1 at node X2 K2 in bracket X1 minus X2 is equal to M2 d square X2 by dt square. So taking Laplace of above equation and the equation becomes K2 in bracket X1 of s minus X2 of s is equal to M2 s square X2 of s. So this is the equation 2 step 4 and 5. So we have to use the force voltage analogy in mathematical modeling at node X1 from equation 1 we can write down this equation. So these are the analogous equivalent terms we can use in FV analogy already we know that and according to that we have to write down the equation. Here the force is replaced by V and M is replaced by L, B is replaced by R, K is replaced by 1 by C and the X of s is replaced by I of s upon s. So the equation becomes V of s is equal to L1 s square I1 of s upon s plus R s I1 of s upon s plus 1 by C1 I1 of s upon s plus 1 by C2 in bracket I1 of s upon s minus I2 of s upon s. After simplification we are getting this equation and this is equation 3. Now we have to write down the equation at node X2. So from equation 2 here again we have to replace the terms. So K is replaced by 1 by C and the X of s is replaced by I of s upon s 1 by C2 in bracket I1 of s upon s minus I2 of s upon s is equal to L2 s square I2 of s upon s and after simplification we are getting this equation at node X2 that is equation 4. Now we see the conversion of mechanical to electrical system in force voltage analogy. Already we know that in force voltage analogy output is in terms of current. So connections are in series or we can say that from equation 3 and 4 we can draw the circuit also. So first we see this is the mechanical system. Mechanical system those elements are connected in parallel get connected in series in electrical system and those are connected in series in mechanical system get connected in parallel in electrical system. So these elements are connected in series and these two are connected in parallel. So here the L1 is equivalent to M1, R is equivalent to B, C1 is equivalent to 1 by K1 and C2 is equivalent to 1 by K2 and the L2 is equivalent to M2. Now we see the steps 6 and 7 that is nothing but force current analogy in mathematical modeling. So at node X1 or from equation 1 here in force current analogy the force is replaced by current, mass it is replaced by C, B is replaced by 1 by R, K is replaced by 1 by L, X of S is replaced by V of S upon S. So since force current analogy we have to write down the equation in terms of current. So I of S is equal to C1 S square V1 of S upon S plus 1 by K V1 of S upon S plus 1 by L2 V1 of S upon S plus 1 by L2 in bracket V1 of S upon S minus V2 of S upon S. So after simplification we are getting this equation that is equation 5. At node X2 from equation 2 this is the equation. So here instead of K I am writing 1 by L and instead of X of S I am writing V of S upon S. So the equation becomes 1 by L2 in bracket V1 of S upon S minus V2 of S upon S is equal to C2 S square V2 of S upon S. So after simplification we are getting equation 6 that is equation in terms of current at node X2. Now version of mechanical to electrical system in force current analogy. So in force current analogy output is in terms of voltage. So connections are in parallel or from equation 5 and 6 we can draw the electrical system. So this is mechanical system. Here the M1 B and Kverand corrected in parallel. So same elements you have to connected in parallel and these two elements are connected in series. Here C1 is equivalent to M1 then R is equivalent to 1 by B, L1 is equivalent to 1 by K1 and L2 is equivalent to 1 by K2 and the C2 is equal to M2. So here we have to convert mechanical to electrical system in force current analogy. These are the references of this video lecture. Thank you.