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

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Question

(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

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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)$$U = \frac{1}{2} m \omega^2 x^2$Given that $K = \frac{1}{n} U$,we substitute the expressions:$\frac{1}{2} m \omega^2 (A^2 - x^2) = \frac{1}{n} (\frac{1}{2} m \omega^2 x^2)$$A^2 - x^2 = \frac{x^2}{n}$$A^2 = x^2 + \frac{x^2}{n} = x^2 (1 + \frac{1}{n})$$A^2 = x^2 (\frac{n+1}{n})$$x^2 = A^2 (\frac{n}{n+1})$$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 $A$,what is the displacement of the particle?

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