A particle executes simple harmonic motion between and . If the time taken by the particle to go from to is , then the time taken by the particle in going from to is [2023]

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Solution

Q.
A particle executes simple harmonic motion between $x = - A$ and $x = + A$ . If the time taken by $A$ the particle to go from $x = 0$ to $\frac{A}{2}$ is $2 s$ , then the time $A$ taken by the particle in going from $x = \frac{A}{2}$ to $A$ is [2023]

1 1.5 s

2 3 s

3 4 s

4 2 s

Ans.
(3)

Let time from 0 to $\frac{A}{2}$ is $t_{1}$ and from $\frac{A}{2}$ to $A$ is $t_{2}$

Then $ω t_{1} = \frac{π}{6}, ω t_{2} = \frac{π}{3}$

$\frac{t_{1}}{t_{2}} = \frac{1}{2}, t_{2} = 2 t_{1} = 2 \times 2 = 4 sec$

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