Question 355: Oscillations

Question

A particle performs simple harmonic motion with period of 3 s . The time taken by it to cover a distance equal to half the amplitude from mean position is [$$\sin 30^{\circ}=0.5$$]

Accepted Answer

The displacement of particle in SHM at any instant,
$$\begin{aligned}
x & =A \sin \omega t \
\frac{A}{2} & =A \sin \omega t \quad\left(	ext { given, } x=\frac{A}{2}ight) \
\sin \omega t & =\frac{1}{2}=\sin \frac{\pi}{6} \Rightarrow \omega t=\frac{\pi}{6}
\end{aligned}$$
$$\begin{array}{lll}
\Rightarrow & \frac{2 \pi}{T} \cdot t=\frac{\pi}{6} & \left(\because \omega=\frac{2 \pi}{T}ight) \
\Rightarrow & \frac{2 \pi}{3} t=\frac{\pi}{6} & (\because T=3 \mathrm{~s}) \
\Rightarrow & t=\frac{1}{4} \mathrm{~s} &
\end{array}$$

Answer

$$\frac{1}{4} \mathrm{~s}$$

Answer

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

Answer

$$\frac{3}{4} \mathrm{~s}$$

Answer

$$\frac{1}{2} \mathrm{~s}$$

Oscillations

A particle performs simple harmonic motion with period of 3 s . The time taken by it to cover a distance equal to half the amplitude from mean position is [$\sin 30^{\circ}=0.5$]

Choose the correct answer: