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A particle executes simple harmonic motion between x = -A and x = +A . If time taken by particle to go from x = 0 to \frac{A}{2} is 2 s ; then time taken by particle in going from x = \frac{A}{2} to A is

Option: 1

4 s


Option: 2

1.5 s


Option: 3

2 s


Option: 4

3 s


Answers (1)


\begin{aligned} & \cos \theta=\frac{A}{2 \times A}=\frac{1}{2}=\cos 60^{\circ} \\ & \theta=60=\frac{\pi}{3} \\ & \phi_0=30=\frac{\pi}{6} \end{aligned}
\begin{aligned} & \mathrm{0} \rightarrow \frac{\mathrm{A}}{2}, \mathrm{t}=\frac{\frac{\pi}{6}}{\frac{2 \pi}{\mathrm{T}}}=\frac{\mathrm{T}}{12}=2 \\ & \mathrm{~T}=24 \\ & \frac{\mathrm{A}}{2} \rightarrow \mathrm{A}, \mathrm{t}=\frac{\pi / 3}{2 \pi / \mathrm{T}}=\frac{\mathrm{T}}{6}=\frac{24}{6}=4 \mathrm{sec} \end{aligned}

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Sumit Saini

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