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# The potential energy of a particle of mass 1 kg in motion along the x-axis is given by U=4(1−cos2x) J. Here x is in meter. The period of small oscillations (in sec) is _______.2πππ2√2π

A
π
B
2π
C
π2
D
2π
Solution
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#### M=1 kgU=4(1−cos2x)F=−dudxF=−4[0−(−sin2x)(2)]F=−8sin2x Na=−8sin2x m/sec2[∵ m=1 kg]⇒ a≃−8(2x)a=−16x [For small x,sinx≈x]⇒ ω2=42ω=4 rad /acT=2πw=π2sec

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