Problem $10\mathrm{.}6$

a$)$ An inverted pendulum with a point mass at the end of the massless rod is on the moon. Determine its stability type if the input is moment $m$ and the output is angle $.$ The spring is unstretched when the pendulum rod is vertical. The spring and damper at the hinge are rotational. Assume small angular displacements. The parameters are: $W=10lb($measured on the moon$),l=24in,k=60lb*i\frac{n}{r}ad,c=30lb*in*\frac{s}{r}ad,$ gravity $=64i\frac{n}{s^2}.$

b$)$ The response of the pendulum to a unit impulse is shown in the plot. Does the plot agree with your answer from part a$)?$ Why or why not?

c$)$ For this system, is it reasonable to assume small displacements? Why or why not?

Answer: a$)$ Unstable