Standing dynamics can be approximated in below. $(40$ points$)$

In the figure below, the standing dynamics$($left$)$ can be approximated to the simple dynamic

model$($right$).$

Derive an equation of motion $(5$ pts $)$

Show that the transfer function is $TF=\frac{}{T}=\frac{1}{100s^2+200(s)+1000}(10pts)$

Find the poles of TF $(10$ pts