Question

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a=0.7x

(b) a= –200x 2

(c) a=–10x

(d) a=100x 3

Answer 1

A motion represents simple harmonic motion if it is governed by the force law:

F = – kx

ma = – k

$∴ a=-\frac{k}{m}x$

Where,

F is the force

m is the mass (a constant for a body)

x is the displacement

a is the acceleration

k is a constant

Among the given equations, only equation a = –10 x is written in the above form with $\frac{k}{m}=10$

Hence, this relation represents SHM.