Consider the mass$-$spring$-$damper system below.

a$)$ Derive the dynamic equations of motion for the system. Find the transfer function from

the input force $f$ to the output $z($position$)$ assuming zero initial conditions. Show all your hand

calculations.

b$)$ Design the system in MATLAB Simulink. Put a screenshot of your Simulink model on

the answer pdf$.$ Simulate the system for unit$-$step input for $20$ seconds for a set of suitable

parameter values. On one figure, draw $f,z$ and $z^{}$ with respect to time $($use $"$To Workspace"

block for drawing; your figure's background should be white color$).$ Comment on the result.