How much is KE for displacement equal to half the amplitude? - Vidyadip

Question

How much is KE for displacement equal to half the amplitude?

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Answer

$\because\text{x}=\frac{\text{A}}{2}$ so,$\text{KE}=\frac{1}{2}\text{m}\omega^2(\text{A}^2-\text{x}^2)$
$\frac{1}{2}\text{m}\omega^2[\text{A}^2-(\frac{\text{A}}{2})^2]$
$=\frac{1}{2}\times\frac{3}{4}[\text{m}\omega^2\text{A}^2]$
$=\frac{3}{4}(\text{KE})_\text{max}$
It is $\frac{3}{4}\text{th}$ of maximum KE.

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