First slide

Simple harmonic motion

Question

The time taken by a particle executing SHM of period T to move from the extreme position to half the maximum displacement is

Moderate

A

$\frac{T}{3}$
B

$\frac{T}{4}$
C

$\frac{T}{8}$
D

$\frac{T}{6}$

Solution

For a particle executing simple harmonic motion starting from extreme position, the equation for displacement is $y = A \cos ω t$
i.e., $\frac{A}{2} = A \cos \frac{2 π}{T} t$ .
On simplifying this we get $\frac{1}{2} = \cos \frac{2 π}{T} t$ . To satisfy this condition, $\frac{π}{3} = \frac{2 π}{T} t$ , i.e. $\frac{T}{6} = t$

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