First slide

Simple hormonic motion

Question

The instantaneous displacement of a simple pendulum oscillator is given by $x = Acos (ω t + \frac{π}{4})$ . 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

$V = \frac{dx}{dt} = - A ω \sin (ω t + \frac{π}{4}) 5, V_{\max} = A ω$
$when V = V_{\max}, ω t + \frac{π}{4} = \frac{π}{2}, \frac{3 π}{2}, \frac{5 π}{2}, \frac{7 π}{2}, . ...$
$∴ t = \frac{1}{ω} (\frac{π}{2} - \frac{π}{4}) = \frac{π}{4 ω}$

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