A body is executing simple harmonic motion. At a displacement ' $x$ ' its potential energy is, $E_1$ and at a displacement ' $y$ ' its potential energy is $E_2$, The potential energy E at a displacement $(x+y)$ is

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Aicharya · Accepted Answer

For a body executing SHM, $\begin{aligned} & E_1=\frac{1}{2} k x^2, E_2=\frac{1}{2} k y^2 \ & 	herefore E=\frac{1}{2} k(x+y)^2=\frac{1}{2} k\left(x^2+y^2+2 x yight) \ & =\frac{1}{2} k x^2+\frac{1}{2} k y^2+2\left[\frac{1}{2} k(\sqrt{x y})^2ight] \ & =E_1+E_2+2 \sqrt{E_1 E_2}=\left(\sqrt{E_1}+\sqrt{E_2}ight)^2 \ & 	herefore \sqrt{E}=\sqrt{E_1}+\sqrt{E_2} \end{aligned}$

A body is executing simple harmonic motion. At a displacement ' $x$ ' its potential energy is, $E_1$ and at…

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