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Question

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, then its time period T is

A
Proportional to
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B
Independent of a
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C
Proportional to
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D
Proportional to
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Solution

The correct option is A Proportional to
V=k|x|3F=dvdx=3k|x|2 ........(1)
The equation of simple harmonic motion is given as
x=asinωtmd2xdt2=m(aω2sinωt)=mω2x ..........(2)
Using (i) and (ii), we obtain3k|x|2=mω2xω=3kxmT=2πm3kxT=2πm3kasinωtT1a


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