In the figure on the right, the system is initially at equilibrium. A person

drops a steel ball of mass $m_s$ onto the center of mass $M_l$ from a height $d$

and catches the ball on the first bounce. The ball strikes the mass at time

$t=0$ and the collision is perfectly elastic. The ICs are $x(0^{-})=0$ and

$x^{}(0^{-})=0.$

a$)$ Obtain the transfer function $x\frac{s}{F}(s),$ where $f(t)$ represents the impulse due to the

impact collision.

b$)$ If $m=1kg,b=1N\frac{m}{s},$ and $k=1\frac{N}{m},$ determine the output $x(t)$ analytically, and plot

it$.$

c$)$ Write MATLAB code to obtain the response, and plot it on the same plot. Do your plots

agree?