Question $1$:

Consider the mechanical system shown below. The

displacement $x$ of the mass $m$ is measured from the equilibrium

position. The external force $f(t)$ is the input and $x$ is the output.

$1-$ Derive the Transfer Function of the system X$($S$)/$Y$($S$)$

$2-$ Draw the block diagram

The equation of motion for the system is:

$m{x}^{}+b{x}^{}+kx=f(t)$