In which situation of a body performing simple harmonic motion, t… - Vidyadip

Question

In which situation of a body performing simple harmonic motion, the velocity is half of the maximum velocity?

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Answer

Given : $\text v=\frac{1}{2} \text v_{\max }$
$\text {We know}\quad v=\omega \sqrt{A^2-x^2} $
$\begin{aligned}\text {On squaring}\quad v^2 & =\omega^2\left(A^2-x^2\right)\end{aligned}$
Has been given $\quad v=\frac{v_{\max }}{2}=\frac{A \omega}{2}$
By substituting the values in the above equation
$\begin{aligned}\frac{\omega^2 A^2}{4} & =\omega^2\left(A^2-x^2\right) \\\frac{A^2}{4} & =A^2-x^2 \\x^2 & =\frac{3 A^2}{4} \\x & = \pm \frac{\sqrt{3}}{4} A\end{aligned}$

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