What is meant by angular harmonic oscillation? Compute the time period of angular harmonic oscillation.

Discuss the simple pendulum in detail.

Describe the vertical oscillations of a spring.

Discuss in detail the energy in simple harmonic motion.

Consider the Earth as a homogeneous sphere of radius R and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is \(T=2\pi \sqrt { \frac { R }{ g } } \).