The variations of potential energy $(U)$ with position $x$ for three simple harmonic oscillators $A, B$ and $C$ are shown in figure. The oscillators have same mass. The time period of oscillation is greatest for
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(c)
$U=\frac{1}{2} k x^2$
$x^2=\frac{2 U}{k}$
or $x \propto \frac{1}{k}$ (Since $U$ is constant)
Also $T=2 \pi \sqrt{\frac{m}{k}}$
or $T \propto \frac{1}{\sqrt{k}}$
Therefore $x \propto T$
Hence the oscillation with maximum $x$ will have the maximum time period.
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