In this computer assignment you are asked to simulate the response of a system in computer. You can use either matlab or excel for your computer assignment. INTRO: The system to be simulated is given by a transfer function (TF) as: G(s)= X(s) where Xm(s) is position of the mass and Xw(s) is the position of the wall. The physics of the system is given in the figure below. As shown, a mass is being pushed by a wall. Therefore, input to the system is the wall position, x(). As the wall pushes the mass to the right, due to spring and the dashpot elements the mass does not move same as the wall. The objective is to simulate the mass position X(t) for a given wall position. System parameters are given as M= 10, C=25 and K = 1000. Wall Position Xw(t) Spring Coeff: K Viscous Domper: C Cs+K Ms+Cs+K dx(t) dx(k). dt dt Mass : M Moss Position X(t) TASKS: In the class we have learnt about the Euler's backward differentiation technique for computing derivatives of a signal based on discrete measurements. For example; for a signal x(t) we can compute its derivative at a sample k as the difference between current (k) and previous (k-1) displacement measurements: = x(k)= Surface x(k)-x(k-1) T, where I, is the sampling time. This approach has been fundamental for implementing any controller on a micro computer. Please use this approach and do the following. 1) Derive the differential equation for the system given by the TF above. 2) Discretize the differential equation using Euler's Backward differentiation and find the expression for current mass position xm (k) in terms of current or past wall or the past mass positions, i.e. xm(k) = ?. 3) Next, assume that the wall position is a sudden step of 1 and that the sampling time is T, = 1 msec. Develop a computer algorithm in Matlab or Excel to simulate the response of the mass position for such input. 4) Plot the wall and mass position for a duration of 5 [sec].