Question

The instantaneous displacement of a simple pendulum oscillator is given by $x = A\cos\left( \omega t + \frac{\pi}{4} \right)$. Its speed will be maximum at time

• A. $\frac{\mathbf{\pi}}{\mathbf{4\omega}}$
• B. $\frac{\mathbf{\pi}}{\mathbf{2\omega}}$
• C. $\frac{\pi}{\omega}$
• D. $\frac{2\pi}{\omega}$

Answer 1

Answer: (A)

$\frac{\mathbf{\pi}}{\mathbf{4\omega}}$

Answer 2

$x = A\cos\left( \omega t + \frac{\pi}{4} \right)$ and $v = \frac{dx}{dt} = - A\omega\sin\left( \omega t + \frac{\pi}{4} \right)$

For maximum speed,

$\sin\left( \omega t + \frac{\pi}{4} \right) = 1$⇒$\omega t + \frac{\pi}{4} = \frac{\pi}{2}$or$\omega t = \frac{\pi}{2} - \frac{\pi}{4}$⇒ $t = \frac{\pi}{4\omega}$