A particle executes S.H.M. of amplitude A along x -axis. At t = 0 , the position of the particle is x = A 2 and it moves along positive x -axis. The displacement of particle in time t is x = A sin ω t

Question

A particle executes S.H.M. of amplitude A along x -axis. At t = 0 , the position of the particle is x = A 2 and it moves along positive x -axis. The displacement of particle in time t is x = A sin ω t + δ , then the value δ will be

TestHub · Accepted Answer

Given, the instantaneous equation of motion of the particle is
$x = A \sin (ω t + δ) . . . (1)$
As the particle is moving along positive $x$ -axis, $v = \frac{d x}{d t} > 0$ .
Substitute $0$ for $t$ and $\frac{A}{2}$ for $x$ into equation (1) and solve to calculate the required phase difference.
$\begin{array}{rcl} \frac{A}{2} & = & A \sin (ω \times 0 + δ) \\ \Rightarrow & \sin δ = \frac{1}{2} \\ = & \sin \frac{π}{6} \\ \Rightarrow & δ = \frac{π}{6} \end{array}$

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