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Question

The Kinetic energy of a particle in SHM is E when the particle passes through the mean position. If its mass is m and amplitude A, the time period is:

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Solution

In case of linear SHM,
Kinetic energy at mean position is maximum. So,
E=m2(vmax)2
Also, vmax=Aω. So,
E=m2(Aω)2
2EmA2=ω2
ω=A2Em
As ω=2πf
ω=2πT. So,
2πT=(2Em)1A
2(πA)m(E)1/2=T
T=(2Em)1/2πA.

1133017_1158735_ans_8d3ddd6be3ba4e18b3df2e23d3dbfae2.jpg

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