A bar of known length L and known mass m is

connected to a spring of known stiffness k. A known

moment Mo is applied as shown. The spring is

unstretched when the bar is vertical and it has a free

length of Lo. The spring always remains horizontal as

the bar rotates.

a) Determine the full nonlinear equation of motion

for the bar in terms of its angle of rotation

measured from the bar's vertical position.

b) Linearize around the bar's vertical position.