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 AProportional to V=k|x|3F=−dvdx=−3k|x|2 ........(1) Theequationofsimpleharmonicmotionisgivenas x=asinωt⇒md2xdt2=m(−aω2sinωt)=−mω2x ..........(2) Using(i)and(ii),weobtain3k|x|2=mω2x⇒ω=√3kxm⇒T=2π√m3kx⇒T=2π√m3kasinωt⇒T∝1√a