# A simple harmonic oscillator has an amplitude a and time period T. The time required to travel from $x= \frac{a}{2}$  is Option 1) $\frac{T}{6}$ Option 2) $\frac{T}{2}$ Option 3) $\frac{T}{4}$ Option 4) $\frac{T}{3}$

As we discussed in concept

Phase -

The quantity $\phi = wt+\delta$ is called the phase . It determines the status of the particle in simple harmonic motion.

- wherein

e.g.

$x= A\sin \left ( wt +\delta \right )\rightarrow$ phase

$x=A\sin (wt+\frac{\pi }{2})$

$x=\frac{A}{2}$

$\frac{A}{2}=A\sin (wt+\frac{\pi }{2})$

$\frac{1}{2}=\cos wt$

$=>wt=\frac{\pi }{3}$

$\frac{2\pi }{T}t=\frac{\pi }{3}$

$=>t=\frac{T}{6}$

Option 1)

$\frac{T}{6}$

Option is Correct

Option 2)

$\frac{T}{2}$

Option is incorrect

Option 3)

$\frac{T}{4}$

Option is incorrect

Option 4)

$\frac{T}{3}$

Option is incorrect

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