The kinetic energy of SHM is 1/n times its po | vedclass

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(C) The kinetic energy $K$ and potential energy $U$ of a particle in $SHM$ at displacement $x$ are given by:$K = \frac{1}{2} m \omega^{2} (A^{2} - x^{

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$\sqrt{\frac{n}{n+1}} A$

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(C) The kinetic energy $K$ and potential energy $U$ of a particle in $SHM$ at displacement $x$ are given by:$K = \frac{1}{2} m \omega^{2} (A^{2} - x^{2})$$U = \frac{1}{2} m \omega^{2} x^{2}$Given that $K = \frac{1}{n} U$,we substitute the expressions:$\frac{1}{2} m \omega^{2} (A^{2} - x^{2}) = \frac{1}{n} \left( \frac{1}{2} m \omega^{2} x^{2} \right)$$A^{2} - x^{2} = \frac{x^{2}}{n}$$A^{2} = x^{2} + \frac{x^{2}}{n} = x^{2} \left( 1 + \frac{1}{n} \right) = x^{2} \left( \frac{n+1}{n} \right)$$x^{2} = A^{2} \left( \frac{n}{n+1} \right)$$x = \sqrt{\frac{n}{n+1}} A$

The kinetic energy of $SHM$ is $1/n$ times its potential energy. If the amplitude of the $SHM$ is $A$,then what is the displacement of the particle?

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