Question 264: Oscillations

Question

For a particle executing S.H.M. having amplitude A, the speed of the article is $\left(\frac{1}{3}ight)^{	ext {rd }}$ of its maximum speed when the displacement from the mean position is

Accepted Answer

$$\begin{aligned}
& V=\omega \sqrt{A^2-x^2} \quad	ext{.... (i)}\
& V_{\max }=\omega A \
& V=\frac{V_{\max }}{3}=\frac{\omega a}{3} \
& \frac{\omega A}{3}=\omega \sqrt{A^2-x^2} \quad	ext{... [From (i)]}\
& \frac{A^2}{9}=\left(A^2-x^2ight) \
& x^2=A^2-\frac{A^2}{9} \
& x=\sqrt{\frac{8}{9} A^2} \
& x=\frac{2 \sqrt{2}}{3} A
\end{aligned}$$

Answer

$\frac{3 \mathrm{~A}}{\sqrt{2}}$

Answer

$\frac{2 \mathrm{~A}}{3}$

Answer

$\frac{2 \sqrt{2}}{3} \mathrm{~A}$

Answer

$\frac{\sqrt{2}}{3} \mathrm{~A}$

Oscillations

For a particle executing S.H.M. having amplitude A, the speed of the article is \left(\frac{1}{3}\right)^{\text {rd }} of its maximum speed when the displacement from the mean position is

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