First slide

Simple harmonic motion

Question

A particle executing SHM 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

$1 / 3 \sec$
C

$2 / 3 \sec$
D

$\sqrt{3 / 2} \sec$

Solution

Equation of motion $y = a \cos ω t$
$\begin{array}{l} \Rightarrow \frac{a}{2} = a \cos ω t \Rightarrow \cos ω t = \frac{1}{2} \Rightarrow ω t = \frac{π}{3} \\ \Rightarrow \frac{2 π t}{T} = \frac{π}{3} \Rightarrow t = \frac{\frac{π}{3} \times T}{2 π} = \frac{4}{3 \times 2} = \frac{2}{3} \sec \end{array}$

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