A particle executes simple harmonic between `x=-A` and `x=+A`.If time taken by particle to go from `x=0` to `(A)/(2)` is `2` s, then time taken by particle in going from `x=(A)/(2)` to `A` is

Options

A. `1.5s`
B. `3s`
C. `4s`
D. `2s`

Answer

To solve the problem, we need to analyze the motion of a particle executing simple harmonic motion (SHM) between the positions \( x = -A \) and \( x = A \).

### Step-by-Step Solution:

1. **Understanding SHM**: In SHM, the particle moves back and forth between two extreme positions, which are \( -A \) and \( A \). The mean position is at \( x = 0 \).

2. **Time taken from \( x = 0 \) to \( x = \frac{A}{2} \)**: We are given that the time taken for the particle to move from the mean position \( x = 0 \) to \( x = \frac{A}{2} \) is \( 2 \) seconds.

3. **Total time for a quarter of the cycle**: In SHM, the time taken to move from the mean position to the extreme position (from \( x = 0 \) to \( x = A \)) is a quarter of the total time period \( T \) of the motion. Therefore, the time taken to go from \( x = 0 \) to \( x = A \) is \( \frac{T}{4} \).

4. **Time taken from \( x = 0 \) to \( x = A \)**: Since the time taken from \( x = 0 \) to \( x = \frac{A}{2} \) is \( 2 \) seconds, the time taken from \( x = \frac{A}{2} \) to \( x = A \) will also be \( 2 \) seconds. This is because the motion is symmetrical in SHM.

5. **Conclusion**: Therefore, the time taken by the particle to go from \( x = \frac{A}{2} \) to \( x = A \) is also \( 2 \) seconds.

### Final Answer:
The time taken by the particle in going from \( x = \frac{A}{2} \) to \( A \) is \( 2 \) seconds.

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