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.
A$\frac{1}{4}$
B$\frac{1}{3}$
C$\frac{3}{4}$
D$\frac{1}{2}$
JEE MAIN 2021, Medium
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C$\frac{3}{4}$
c $K =\frac{1}{2} m \omega^{2}\left( A ^{2}- x ^{2}\right)$
$=\frac{1}{2} m \omega^{2}\left( A ^{2}-\frac{ A ^{2}}{4}\right)$
$=\frac{1}{2} m \omega^{2}\left(\frac{3 A ^{2}}{4}\right)$
$K =\frac{3}{4}\left(\frac{1}{2} m \omega^{2} A ^{2}\right)$
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