Explanation:
Let ' \(y\) ' be the distance where kinetic energy equals to potential energy.
Kinetic energy of \(SHM\) is
\(\Rightarrow\) K.E. \(=\dfrac{1}{2} k\left(A^{2}-y^{2}\right)\), where \(K\) is a
constant.\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
Potential energy of \(SHM\) is
\( \Rightarrow P.E.{\rm{ }} = \frac{1}{2}k{y^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
By equating (1) and (2)
\(\begin{aligned}& \dfrac{1}{2} k\left(A^{2}-y^{2}\right)=\dfrac{1}{2} k y^{2} \\& \dfrac{1}{2} k A^{2}=k y^{2} \Rightarrow y=\dfrac{A}{\sqrt{2}}\end{aligned}\)