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Question

In an angular simple harmonic motion angular amplitude of oscillation is $$\pi$$ rad and time period is $$0.4$$ sec then calculate its angular velocity at angular displacement $$\pi/2$$ rad.


A
34.3 rad/sec
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B
42.7 rad/sec
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C
22.3 rad/sec
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D
50.3 rad/sec
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Solution

The correct option is B $$\text{42.7 rad/sec}$$
$$\theta=\theta_A \sin (wt)$$
$$\theta=\pi \sin \left(\dfrac{2\pi}{0.4}t\right)\rightarrow (i)$$
$$w=\dfrac{d\theta}{dt}=\pi\times \dfrac{2\pi}{0.4} \cos\left(\dfrac{2\pi}{0.4}t\right)$$
$$\downarrow$$                                      $$\hookrightarrow  (ii)$$
Angular velocity
put $$\theta=\dfrac{\pi}{2}$$ in eq $$(i)$$
$$\sin\left(\dfrac{2\pi}{0.4}t\right)=\dfrac{1}{2}$$
$$\dfrac{2\pi}{0.4}t=\dfrac{\pi}{6}$$
$$t=0.4/12$$
putting $$t=0.4/12$$ in eq $$(ii)$$
$$w=\dfrac{2\pi^2}{0.4}\cos \left(\dfrac{2\pi}{0.4}\times \dfrac{0.4}{12}\right)$$
$$\Rightarrow \dfrac{2\pi^2}{0.4}\times \dfrac{\sqrt{3}}{2}=42.7\ rad/sec$$
Option $$(B)$$

Physics

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