Question

Which of the following exhibits simple harmonic motion?
I) A pendulum
II) A mass attached to a spring
III) A ball bouncing up and down, in absence of friction
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

Answer 1

A simple harmonic force (SHM) is a type of oscillatory motion. The object under a simple harmonic motion experiences a retarding force that is proportional to the amount of displacement from the equilibrium position. It is a back and forth motion through a central position.

Complete solution:
When a mass is attached to a spring, the restoring forces are directly proportional to displacement of the mass therefore it can be considered as a SHM. The restoring force according to Hooke’s Law is $F = k \times x$, where $x$ is the displacement and $k$ is the spring constant.
In the motion of a pendulum, the restoring forces that act are directly proportional to the angle of displacement made by the bob from the equilibrium position which is at the center. The damping in the motion is due to the air drag, therefore it will be more correct to call it a damped harmonic motion rather than a SHM.
A ball bouncing up and down definitely exhibits an oscillatory motion but not a simple harmonic motion as the displacement of the ball from any point is not proportional to any of the forces that is acting on it i.e. it’s weight and the elastic force that is responsible for the bounce.

The correct answer is (B), II only.

Note: Simple harmonic motion is often confused with oscillatory motion. They are only a category of oscillatory motion and have some extra qualities. The retarding force in it must be proportional to its displacement from the equilibrium position.