Q. A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :

Solution:

Potential energy $(U) = \frac{1}{2} kx^2$
Kinetic energy $(K) = \frac{1}{2} kA^2 - \frac{1}{2} kx^2$
According to the question, U = k
$\therefore \frac{1}{2} kx^{2} = \frac{1}{2} kA^{2} - \frac{1}{2} kx^{2}$
$ x = \pm \frac{A}{\sqrt{2}} $
$\therefore$ Correct answer is (3)

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