First slide

Simple harmonic motion

Question

The instantaneous displacement of a simple pendulum oscillator is given by $x = Acos (ωt + \frac{π}{4})$ . Its speed will be maximum at time

Moderate

A

$\frac{π}{4 ω}$
B

$\frac{π}{2 ω}$
C

$\frac{π}{ω}$
D

$\frac{2 π}{ω}$

Solution

$x = Acos (ωt + \frac{π}{4})$ and $v = \frac{dx}{dt} = - Aωsin (ω t + \frac{π}{4})$
For maximum speed, $\sin (ω t + \frac{π}{4}) = 1$ $\Rightarrow ω t + \frac{π}{4} = \frac{π}{2}$ or $ω t = \frac{π}{2} - \frac{π}{4}$ $\Rightarrow t = \frac{π}{4 ω}$

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