2. Consider the mechanical system depicted below. The input is given by f(t), and the output is y(t). (1) Determine the transfer function from f(t) to y(t) and plot the system response to a unit step input. Let m = 10, k=1, and b=0.5. Show that the peak amplitude of the output is about 1.8. (2) Determine the damping ratio and the natural frequency for the system. (3) Is this system over-damped, critically damped or underdamped? Justify your answer. (4) For a Mass m=10, choose values for b and k to yield the same natural frequency as original system but is critically damped. f(1) Forcing function Spring constant k Mass m Mass displacement y(t) Friction constant b