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  4. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A / 2, the kinetic energy of the block is

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Q. The maximum potential energy of a block executing simple harmonic motion is $25 \,J$. A is amplitude of oscillation. At $A / 2$, the kinetic energy of the block is

JEE MainJEE Main 2023Oscillations

Solution:

$u _{\max }=\frac{1}{2} m \omega^2 A ^2=25 J$
$KE$ at $\frac{ A }{2}=\frac{1}{2} m v_1^2=\frac{1}{2} m \omega^2\left(A^2-\frac{A^2}{4}\right)$
$KE =\frac{1}{2} m \omega^2 \frac{3 A ^2}{4}=\frac{3}{4}\left(\frac{1}{2} m ^2 A ^2\right) $
$KE =\frac{3}{4} \times 25=18.75\, J$