Question 11: Oscillations

Question

A particle is performing simple harmonic motion. Equation of its motion is $$x = 5\sin \left( {4t - {\pi  \over 6}} \right),x$$ being the displacement from mean position. Velocity (in ms$$^{-1}$$) of the particle at the instant when its displacement is 3, will be

Accepted Answer

According to the question,
$$x=5 \sin \left(4 t-\frac{\pi}{6}ight)$$
When $$x=3$$,
$$\begin{aligned}
& \Rightarrow \quad \frac{3}{5}=\sin \left(4 t-\frac{\pi}{6}ight) \
& \Rightarrow \quad 4 t-\frac{\pi}{6}=37^{\circ} \
& 	ext { Hence, velocity }=\frac{d x}{d t}=5 	imes 4 \cos \left(4 t-\frac{\pi}{6}ight) \
& =5 	imes 4 	imes \cos 37^{\circ} \
& =16 \mathrm{~ms}^{-1} \
& \left(\because \cos 37^{\circ}=\frac{4}{5}ight) \
&\end{aligned}$$

Answer

$${{2\pi } \over 3}$$

Answer

$${{5\pi } \over 6}$$

Answer

20

Answer

16

Oscillations

A particle is performing simple harmonic motion. Equation of its motion is $x = 5\sin \left( {4t - {\pi \over 6}} \right),x being the displacement from mean position. Velocity (in ms^{-1}$) of the particle at the instant when its displacement is 3, will be

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