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. $\text{34.3 rad/sec}$
• B. $\text{42.7 rad/sec}$
• C. $\text{22.3 rad/sec}$
• D. $\text{50.3 rad/sec}$

Answer 1

The correct option is B $\text{42.7 rad/sec}$

$\theta ={\theta }_A\sin \left(wt\right)$

$\theta =\pi \sin \left(\frac{2\pi }{0.4}t\right)\to \left(i\right)$

$w=\frac{d\theta }{dt}=\pi \times \frac{2\pi }{0.4}\cos \left(\frac{2\pi }{0.4}t\right)$

$\downarrow$ $\hookrightarrow \left(ii\right)$

Angular velocity

put $\theta =\frac{\pi }{2}$ in eq $\left(i\right)$

$\sin \left(\frac{2\pi }{0.4}t\right)=\frac{1}{2}$

$\frac{2\pi }{0.4}t=\frac{\pi }{6}$

$t=0.4/12$

putting $t=0.4/12$ in eq $\left(ii\right)$

$w=\frac{2{\pi }^2}{0.4}\cos (\frac{2\pi }{0.4}\times \frac{0.4}{12})$

$\Rightarrow \frac{2{\pi }^2}{0.4}\times \frac{\sqrt{3}}{2}=42.7rad/sec$

Option $\left(B\right)$