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Q. In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

JEE MainJEE Main 2021Oscillations

Solution:

$K=\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)$
$=\frac{1}{2} m \omega^{2}\left(A^{2}-\frac{A^{2}}{4}\right)$
$=\frac{1}{2} m \omega^{2}\left(\frac{3 A^{2}}{4}\right)$
$K=\frac{3}{4}\left(\frac{1}{2} m \omega^{2} A^{2}\right)$