A particle of mass is executing oscillations about the origin on the axis

PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A particle of mass

m

is executing oscillations about the origin on the

x

axis. Its potential energy is

V(x) = k|x|^3

where

k

is a positive constant. If the amplitude of oscillation is

a

, find its time period

T

. (1) proportional to

1/\sqrt{a}

(2) independent of

a

(3) proportional to

\sqrt{a}

(4) proportional to

a^{3/2}