Question $2$

In the given mass$-$spring$-$damper system, the position $x(t)$ is the excitation $($or input$)$ signal and the velocity $v_m(t)$ of the mass is the output signal.

Questions:

$($a$)$ Determine the transfer function of this system.

$($b$)$ Take $m=2kg,c=22N\frac{s}{m}$ and $k=20\frac{N}{m}.$ Draw the Bode plot of this system on the next page.

$($c$)$ If $x(t)=sin(t),$ what will $v_m(t)$ be equal to once the transient has disappeared?