First slide

Periodic Motion

Question

A simple harmonic oscillator has an amplitude a and time period T. The time required to travel from $x = a to$ $x = a / 2 is$

Moderate

A

T/6
B

T / 4
C

T/3
D

T/2

Solution

$x = asin ωt = asin (\frac{2 π}{T}) t Now \frac{a}{2} = asin (\frac{2 π}{T}) t or \sin (\frac{2 π}{T}) t = \frac{1}{2} or sim (\frac{2 π}{T}) t = \sin \frac{π}{6} or t = T / 12 For x = a we have t = T / 4 So, the time taken to travel from x = a to x = a / 2 = T / 4 - T / 12 = T / 6$

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