Q.

An object of mass 4 kg is moving along X-axis and its potential energy as a function of x can be expressed as U(x) = 4 (1- cos 2x) joule then time period for small oscillations is:

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a

π2 sec

b

π4 sec

c

π sec

d

3π2 sec

answer is C.

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Detailed Solution

F=-dUdx=-4×2 sin 2x For small oscillations, sin 2x≈2x                              F=-16x⇒a=Fm=-4x                               ω2=4⇒T=π sec
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An object of mass 4 kg is moving along X-axis and its potential energy as a function of x can be expressed as U(x) = 4 (1- cos 2x) joule then time period for small oscillations is: