A particle of mass $m$ in a unidirectional potential field have potential energy $U(x)=\alpha+2 \beta x^2$, where $\alpha$ and $\beta$ are positive constants. Find its time period of oscillation.
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(c)
$U(x)=\alpha+2 \beta x^2$
$F=-\frac{d U(x)}{d x}$
$F=-4 \beta x$
$T=2 \pi \sqrt{\frac{m}{k}}$
$T=2 \pi \sqrt{\frac{m}{4 \beta}} \quad \cos [k=\beta]$
$T=\pi \sqrt{\frac{m}{\beta}}$
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