First slide

Simple hormonic motion

Question

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

Moderate

A

1 s
B

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

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

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

Solution

Equation of motion, $y = A \cos ωt$
$\Rightarrow$ $\frac{A}{2} = A \cos ωt \Rightarrow ωt = \frac{π}{3}$
$\Rightarrow$ $\frac{2 πt}{T} = \frac{π}{3} \Rightarrow t = \frac{\frac{π}{3} \times T}{2 π} = \frac{4}{3 \times 2} = \frac{2}{3} s$

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