Question $2$:

For the mechanical system below, the uniform rigid bar has mass $m$ and pinned at point O $.$ For this system:

a$)$ find the equation of motion using newton's second law.

b$)$ Identify the damping ratio and natural frequency in terms of the parameters $m,c,k,$ and $l.$

c$)$ For: $m=1\mathrm{.}60kg,l=60cm,c=0\mathrm{.}1250(\frac{m}{s}),k=260\frac{N}{m},$ find the angular displacement of the bar $(t)$ for the following initial conditions:

$(0)=0,$

$(0)=10ra\frac{d}{s}.$

Assume that in the horizontal position the system is in static equilibrium and that all angles remain small.