For the spring damper system shown, let $k=200\frac{N}{m},$

$b=20N^{*}\frac{s}{m},$ and $m=0kg.$

a$.$ Create a free body diagram.

b$.$ Find a system equation in terms of the

displacement of the massless junction $($hint: use

a newton's law equation with zero mass$).$

c$.$ Solve and sketch the system response if $x(0)=$

$0\mathrm{.}3$ m and $f(t)=20N$

d$.$ Sketch the plot of the spring and damper forces

over time for the case described in part c$).$

Note: plots should go from time zero to steady

state. Be sure to comment on the reasonableness of the plots.