First slide

Simple hormonic motion

Question

A particle executes SHM with a time period of 4 s. Find the time taken by the particle to go directly from its mean position to half of its amplitude.

Moderate

A

$\begin{array}{rcl} \frac{1}{2} s \end{array}$
B

$\begin{array}{rcl} 1 s \end{array}$
C

$\begin{array}{rcl} \frac{1}{4} s \end{array}$
D

$\begin{array}{rcl} \frac{1}{3} s \end{array}$

Solution

$\begin{array}{rcl} x & = & A \sin (ωt) \\ \frac{A}{2} & = & A \sin (\frac{2 π}{T} t) \\ ∴ \frac{2 π}{4} t & = & \frac{π}{6} \\ t & = & \frac{1}{3} s \end{array}$

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