Question

In an angular shm angular amplitude of oscillation is pi radian and time period is 0.4 sec then calculate its angular velocity at angular displacement pi/2rad

Answer 1

The answer is 42.4

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Answer 2

The final angular velocity is 42.7 rad/s.

Explanation:

Given that,

Angular amplitude $\theta_{0}= \pi\ rad$

Time period  = 0.4 sec

Angular displacement $\theta=\dfrac{\pi}{2}\ rad$

We need to calculate the initial angular velocity

Using formula of angular velocity

$\omega=\dfrac{2\pi}{T}$

Put the value into the formula

$\omega=\dfrac{2\pi}{0.4}$

$\omega =5\pi\ rad/s$

We need to calculate the final angular velocity

Using formula of angular velocity

$\omega'=\omega\sqrt{\theta_{0}^2-\theta^{2}}$

Put the value into the formula

$\omega'=5\pi\sqrt{\pi^2-(\dfrac{\pi}{2})^2}$

$\omega'=42.7\ rad/s$

Hence, The final angular velocity is 42.7 rad/s.

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Topic : angular velocity

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