Consider the spring$-$mass$-$damper shown in $Fi{g}_g\mathrm{.}1,$ where $\frac{M}{?}$ is the mass of the objec,

$k$ is the spring constant of the ideal spring and $b$ is the friction constant and rin is ble

external applied force $($input$)$ on the mass.

a$.$ Draw the free body diagram and use Newton's second law to determine the

differential equation modeling the dynamics of this system that relates the

input, $r(t)$ to the distance $y(t).$

b$.$ Use Laplace transform and determine $Y(s)$ if the input $r(t)=0,M=1,b=5$ and $k=6,$

$y(0)=4,\frac{dy(t)}{dt}{|}_t=0=0.$

Determine the output $y(t)$ by transforming the $Y(s)$ that you got in part b$)$ to time

domain.