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(C) The potential energy of a simple harmonic oscillator is given by $U = \frac{1}{2} k x^2$,where $k$ is the force constant.For a given potential ene

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$C$

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(C) The potential energy of a simple harmonic oscillator is given by $U = \frac{1}{2} k x^2$,where $k$ is the force constant.For a given potential energy $U$,the displacement $x$ is given by $x = \sqrt{\frac{2U}{k}}$,which implies $x \propto \frac{1}{\sqrt{k}}$.The time period of oscillation is $T = 2 \pi \sqrt{\frac{m}{k}}$.Since the mass $m$ is the same for all oscillators,we have $T \propto \frac{1}{\sqrt{k}}$.Comparing the two relations,we get $T \propto x$ for a constant value of $U$.From the figure,the maximum displacement (amplitude) $x$ is greatest for oscillator $C$.Therefore,the time period of oscillation is greatest for $C$.

The variations of potential energy $(U)$ with position $x$ for three simple harmonic oscillators $A, B$ and $C$ are shown in the figure. The oscillators have the same mass. The time period of oscillation is greatest for

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