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Question

A particle of mass m is executing oscillations about the origin on the x-axis. It's potential energy is U(x)=k|x|3, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is:

A
proportional to 1a
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B
independent of a
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C
proportional to a
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D
proportional to a3/2
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Solution

The correct option is A proportional to 1a
U=k|x|3F=dUdx=3k|x|2...(i)
Also, for SHM x=asinωt and d2xdt2+ω2x=0
acceleration a=d2xdt2=ω2xF=ma
=md2xdt2=mω2x...(ii)
From equation (i) & (ii) we get ω=3kxm
T=2πω=2πm3kx=2πm3k(asinωt)T1a

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