First slide

Simple hormonic motion

Question

A particle doing simple harmonic motion, amplitude = 4 cm, time period = 12 sec. The ratio between time taken by it in going from its mean position to 2 cm and from 2 cm to extreme position is

Moderate

A

1
B

$\frac{1}{3}$
C

$\frac{1}{4}$
D

$\frac{1}{2}$

Solution

$ω = \frac{2 π}{T} = \frac{2 π}{12} = \frac{π rad}{6 \sec}$
(For y = 2 cm) 2 = 4( $\sin \frac{π}{6} t_{1}$ )
By solving $t_{1} = 1 \sec$ (For y = 4 cm) $t_{2} = 3 \sec$
So time taken by particle in going from 2 cm to extreme position is $t_{2} - t_{1} = 2 \sec . Hence required ratio will be \frac{1}{2}$

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