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 bythe force law:

F= –kx

ma= –k

Where,

Fis the force

mis the mass (a constant for a body)

xis the displacement

ais the acceleration

kis a constant

Amongthe given equations, only equation a = –10 x iswritten in the above form with Hence, this relation represents SHM.