The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement ( x ) starting from mean position to extreme position ( A ) is given by

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The formula to calculate the kinetic energy of a particle executing SHM is given by

$K = \frac{1}{2} m ω^{2} (A^{2} - x^{2}) . . . (1)$

Substitute $0$ for $x$ into equation (1) to obtain the kinetic energy at the mean position.

$\begin{array}{rcl} K & = & \frac{1}{2} m ω^{2} (A^{2} - 0^{2}) \\ = & \frac{1}{2} m ω^{2} A^{2} \end{array}$

Substitute $A$ for $x$ into equation (1) to obtain the kinetic energy at the end points.

$\begin{array}{rcl} K & = & \frac{1}{2} m ω^{2} (A^{2} - A^{2}) \\ = & 0 \end{array}$

Hence, the variation can be shown as follows-

Physics - SHM Question with Solution | TestHub

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