Consider the following mechanical system:

a) Write a differential equation that describes the motion for this system.

b) Take the Laplace transform of this equation and determine its transfer function G(s), assuming zero initial conditions.

c) Plot the impulse response of this system using the impulse( ) function, with a 40s time axis.

d) Plot the step response of the system using the step( ) function with a 50s time axis.

e) Use the plot obtained in (d) to determine the nature of the system.

f) Confirm your answer in (e) by calculating the damping ratio of the system.

g) Use the plot obtained in (e) to determine damped frequency of the system oscillation and confirm your result through calculations.

h) Damping of the system is reduced by factor 10. Plot the new step response of the system and determine the 95% rise time.