Problem 4. In the figure below, a uniform rigid slider rod with mass m and length l is pinned to
point O. The slender rod is attached to a spring with stiffness k at its end. The slender rod was
given a small initial angular displacement $\theta_0$. Find (symbolically):
a. The equation of motion of the slender rod (ignore the effect of gravity).
b. The natural frequency of the system.
Hint: Here, you will need to be cautious about the relationship between the angular motion of
the slender rod and the deformation of the spring.
Hint 2: Because $\theta$ is very small, you may assume the spring remains vertical throughout the
