Problem #$3$:

Consider the spring$-$loaded inverted pendulum shown below. Assume that the spring force on the

pendulum is zero when the pendulum is vertical, and that friction is negligible. Develop a mathematical

model for the system under the condition of small angles. Determine the natural frequency of the system

$({}_n)$ using:

$($a$)(2$ pts$)$ Newton's second Law $($draw the FBD and show the complete steps$)$

$($b$)$ pts$)$ The energy method