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:

A
$\frac{π}{2} \sec$
B
$\frac{π}{4} \sec$
C
$π \sec$
D
$\frac{3 π}{2} \sec$

Solution:

$F = \frac{- dU}{dx} = - 4 \times 2 \sin 2 x For small oscillations, \sin 2 x \approx 2 x F = - 16 x \Rightarrow a = \frac{F}{m} = - 4 x ω^{2} = 4 \Rightarrow T = π \sec$

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