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  4. For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

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Q. For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

JEE MainJEE Main 2021Oscillations

Solution:

$KE = PE$
$\frac{1}{2} m \omega^{2}\left( A ^{2}- x ^{2}\right)=\frac{1}{2} m \omega^{2} x ^{2}$
$A ^{2}- x ^{2}= x ^{2}$
$2 x ^{2}= A ^{2}$
$x =\pm \frac{ A }{\sqrt{2}}$