First slide

Simple harmonic motion

Question

The following figure shows the displacement versus time graph for two particle s A and B executing simple harmonic motions. The ratio of their maximum velocities is

Moderate

A

3:1
B

1:3
C

1:9
D

9:1

Solution

For A, time period T_A = 16 s (distance between two adjacent crests)
For B, time period $T_{B} = 2 (20 - 8) = 24 s$ (length between the crest and trough shown $= 20 s - 8 s = 12 s)$
Also, amplitudes $a_{A} = 10 cm, a_{B} = 5 cm$
$Now, \frac{{(V_{max})}_{A}}{{(V_{min})}_{B}} = \frac{ω_{A} a_{A}}{ω_{B} a_{B}} = \frac{(\frac{2 π}{T_{A}}) a_{A}}{(\frac{2 π}{T_{B}}) a_{B}} = \frac{T_{B} a_{A}}{T_{A} a_{B}} = \frac{24 \times 10}{16 \times 5} = \frac{3}{1}$

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