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Question

A particle performs S.H.M. whose velocity is v1 at a distance x1 from mean position and velocity is v2 at distance x2 . The time period and amplitude will be.

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Solution

Let the amplitude of the oscillation beAandωbe the angular frequency then,

v21=ω2(A2x21)

v22=ω2(A2x22)

EliminatingAfrom the above equations by subtracting we get

ω2=(v21v22x22x21)

We know

ω=2πT

T=2π(x22x21v21v22)

Hence, the time period is T=2π (x22x21v21v22)


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