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Assertion : In an SHM, kinetic and potential energies become equal when the displacement is \(1 / \sqrt{2}\) times the amplitude.
Reason : In SHM, kinetic energy is zero when potential energy is maximum.
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Reason : In SHM, kinetic energy is zero when potential energy is maximum.
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If both assertion and reason are true but reason is not the correct explanation of assertion
When the displacement of a particle executing SHM is $y$, then its $K . E .=\frac{1}{2} m \omega^2\left(a^2-y^2\right)$ and
$P . E .=\frac{1}{2} m \omega^2 y^2$
For $K . E .=P . E$. or $2 y^2=a^2$ or, $y=a / \sqrt{2}$. Since total energy remains constant through out the motion, which is $E=K . E .+P . E$. So, when P.E. is maximum then $K . E$. is zero and vice versa.
$P . E .=\frac{1}{2} m \omega^2 y^2$
For $K . E .=P . E$. or $2 y^2=a^2$ or, $y=a / \sqrt{2}$. Since total energy remains constant through out the motion, which is $E=K . E .+P . E$. So, when P.E. is maximum then $K . E$. is zero and vice versa.
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