Nsider the system below: (a) Derive the equation of motion of the system using both newton’s second law and the energy method. (b) Assume a value for m, r, J, k and c and plot the response of the system using Matlab or Python. Your code should superimpose the analytical solution on top of the numerically obtained one. Assume initial conditions for your system and F(t) = 0. (c) Change the parameters values in your system so that the system is undamped, overdamped, critically damped and underdamped. Plot the response of the system using Matlab or Python [both analytically and numerically in the same plot]. Assume F(t) = 0. (d) Assume a form for F(t) so that the system is unstable and characterize the type of instability. Plot the solution using Matlab or Python. (e) Assume a form for F(t) so that the system is at (1) resonance and (2) is beating. Plot the solution using Matlab or Python. (f) Solve the equation of motion of the system if