Question

Distinguish between linear and angular harmonic motion .

Answer 1

Linear SHM

From earlier discussion, it is now clear that when a particle is disturbed from its stable equilibrium, it oscillates to and fro about that position.

Let us consider such an oscillation on a straight line. If x represents the displacement of the particle from equilibrium position, then acceleration of the simplest possible motion can be given by

a ∝ − x . . . (1)

i.e. acceleration is always

(i) proportional to the displacement.

(ii) directed towards the equilibrium point.

A motion showing such a feature is known as simple harmonic motion.

Angular SHM

Instead of straight line motion, if particle or centre of mass of body is oscillating on a small arc of circular path, then condition for angular SHM is

Angular acceleration ∝ − (angular displacement) . . . (2)

Force law of SHM

From (1), it follows that

F = ma = − k x . . . (3)

where k is a constant of proportionality

similarly, from (2), for angular SHM

τ = I α = − C θ . . . (4)

where C is a constant of proportionality.

hope this will help u don't forget to mark it a brainliest one