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Question

A particle of mass 4 kg moves in simple harmonic motion and its potential energy U varies with position x as shown in the figure. The time period of oscillation of the particle is 2πα  second. Find the value of α.___


Solution

In SHM, U-x graph is a parabola.
U=C1 x2, where C1 is a constant.
From figure whe, x = 0.2m, U = 2J 
2=C1(0.2)2
C1=20.04=50
U=50x2
Also, in SHM U=12mω2 x2
12mω2=50
ω2=1004=25
ω=5s1
T=2πω=2π5
T=2π5s

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