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Q.

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

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a

1.5s

b

4s

c

3s

d

2s

answer is C.

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Detailed Solution

$\begin{array}{l} y = A \sin ω t \\ \frac{A}{2} = A \sin ω t_{1} \\ \frac{1}{2} = \sin ω t_{1} \\ \frac{π}{2} = \frac{2 π}{T} \times t_{1} \\ t_{1} = \frac{T}{12} t = 2 \sec \\ y = A \\ A = A \sin ω t_{2} \\ 1 = \sin ω t_{2} \\ \frac{π}{2} = ω t_{2} \\ \frac{π}{2} = \frac{2 π}{T} t_{2} \\ t_{2} = \frac{T}{4} \\ t_{2} = \frac{24}{4} = 6 \sec \\ t_{12} = t_{2} - t_{1} = 4 \sec \end{array}$

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