The kinetic energy of $SHM$ is $1/n$ time its potential energy. If the amplitude of the $SHM$ be $A$, then what is the displacement of the particle?
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$\mathrm{K}=\frac{1}{\mathrm{n}} \mathrm{up} \Rightarrow \frac{1}{2} \mathrm{m} \omega^{2}\left(\mathrm{A}^{2}-\mathrm{x}^{2}\right)=\frac{1}{\mathrm{n}} \frac{1}{2} \mathrm{m} \omega^{2} \mathrm{x}^{2}$
that $A^{2}-x^{2}=\frac{x^{2}}{n} \quad$ or $x^{2}\left(1-\frac{1}{n}\right)=A^{2}$
$x=\sqrt{\frac{n}{n+1}} A$
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