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  4. The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25 % more than the potential energy is: cm.

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Q. The amplitude of a particle executing SHM is $3 \,cm$. The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is:_______ $cm$.

JEE MainJEE Main 2023Oscillations

Solution:

$ K E=P E+\frac{P E}{4}$
$K E=\frac{5}{4} P E $
$ \frac{1}{2} m \omega^2\left(A^2-x^2\right)=\frac{5}{4} \times \frac{1}{2} m \omega^2 x^2 $
$ {\left[ v =\omega \sqrt{ A ^2- x ^2}\right]} $
$ A^2-x^2=\frac{5}{4} x^2$
$ \frac{9 x^2}{4}=A^2$
$ x=\frac{2}{3} A $
$ \therefore x=\frac{2}{3} \times 3 cm$
$ x=2 \,cm $