First slide

Simple hormonic motion

Question

A particle executing S.H.M. of amplitude 4 cm and T = 4 sec. The time taken by it to move from positive extreme position to half the amplitude is

Moderate

A

1 sec
B

$\frac{1}{3} \sec$
C

$\frac{2}{3} \sec$
D

$\sqrt{\frac{3}{2}} \sec$

Solution

Equation of motion $y = a \cos ωt$
$\Rightarrow \frac{a}{2} = a \cos ωt \Rightarrow \cos ωt = \frac{1}{2} \Rightarrow ωt = \frac{π}{3}$
$\Rightarrow \frac{2 πt}{T} = \frac{π}{3} \Rightarrow t = \frac{\frac{π}{3} \times T}{2 π} = \frac{4}{3 \times 2} = \frac{2}{3} \sec$

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