Question 345: Oscillations

Question

The displacement from mean position of a particle in SHM at 3 s is $\frac{\sqrt{3}}{2}$ of the amplitude, then its time period is

Accepted Answer

$$ \begin{aligned} &\ &\begin{aligned} & 	ext {  In } \mathrm{SHM}, t=3 \mathrm{~s}, x=\frac{\sqrt{3}}{2} \mathrm{~A} \ & 	herefore \quad x=A \sin \omega t \ & \Rightarrow \quad \frac{\sqrt{3}}{2} A=A \sin (3 \omega) \ & \Rightarrow \quad 3 \omega=\frac{\pi}{3} \ & \Rightarrow \quad \omega=\frac{\pi}{9} \mathrm{rad} / \mathrm{s} \ & 	herefore 	ext { Time period, } T=\frac{2 \pi}{\omega}=\frac{2 \pi}{\frac{\pi}{9}}=18 \mathrm{~s} \end{aligned} \end{aligned} $$

Answer

18 s

Answer

$\frac{6 \sqrt{3}}{2} \mathrm{~s}$

Answer

9 s

Answer

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

Oscillations

The displacement from mean position of a particle in SHM at 3 s is \frac{\sqrt{3}}{2} of the amplitude, then its time period is

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