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A particle of...

Question

A particle of mass m is placed in one-dimensional potential field where potential energy varies as $U (x) = U_{0}$ $(1 - cos b x)$ where $U_{0}$ and b are constants. The period of small amplitude oscillation of the particle is

A

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B

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C

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D

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Solution

The correct option is B
$F = - \frac{d U}{d x} = - U_{0} b sin b x$
$\Rightarrow F = - U_{0} b^{2} x$
$m a = - U_{0} b^{2} x$
$a = - \frac{U_{0} b^{2}}{m} x \Rightarrow T = 2 π \sqrt{\frac{m}{b^{2} U_{0}}}$

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