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Q.

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

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a

$\frac{π}{4 ω}$

b

$\frac{2 π}{ω}$

c

$\frac{π}{2 ω}$

d

$\frac{π}{ω}$

answer is A.

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Detailed Solution

$x = A \sin (ω t + \frac{π}{4})$

$when x = x_{\max}, ω t + \frac{π}{4} = \frac{π}{2}, \frac{3 π}{2}, \frac{5 π}{2}, \frac{7 π}{2}, . ...$

$∴ t = \frac{1}{ω} (\frac{π}{2} - \frac{π}{4}) = \frac{π}{4 ω}$

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The instantaneous displacement of a simple pendulum oscillator is given by x=Asinωt+π4. Its displacement will be maximum at time