First slide

Simple hormonic motion

Question

How long after the beginning of motion is the displacement of a harmonically oscillating point equal to one half of its amplitude, if the period is 24 sec and initial phase is zero?

Moderate

A

12 sec
B

2 sec
C

4 sec
D

6 sec

Solution

$y = A \sin (\frac{2 π}{T} t) When y = \frac{A}{2} then \sin (\frac{2 π}{T} t) = \frac{π}{6} t = \frac{T}{12} = \frac{24}{12} = 2 s$

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