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 = –200x²

(c) a = –10x

(d) a = 100x³

Answer 1

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

F = –kx

ma = –k

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 Hence, this relation represents SHM.