Problem B$-4-1$

Find the transfer function $x_o\frac{s}{x_i}(s)$ of mechanical system shown in figure below. The displacement $x_i$ and $x_o$ are measured from their respective equilibrium positions. Obtain the displacement $x_o(t)$ when the input $x_i(t)$ is a step displacement of magnitude $x_i$ occurring at $t=0.$ Assume that $x_o(0-)=0.$

Solve for the transfer function as instructed. Then, for the response, $x_o(t),$ solve for it using the following system parameters: $x_i(t)=2A*1(t)N,k_1=1\frac{N}{m},k_2=2\frac{N}{m},$ and $c=0\mathrm{.}5N-\frac{s}{m}($Note that the book uses $b_1$ for the damping constant$).$ Lastly, identify the components of the free$/$forced response and the transient$/$steady response in your result.

Figure $4-50$ Mechanical system.