A particle executing simple harmonic motion with an amplitude A. the distance travelled by the particle in one time period is

Options

A. zero
B. A
C. 2A
D. 4A

Explanation

To solve the problem of finding the distance traveled by a particle executing simple harmonic motion (SHM) with an amplitude \( A \) in one time period, we can follow these steps:

### Step 1: Understand the Motion
A particle in simple harmonic motion moves back and forth between two extreme positions, which are at a distance \( A \) from the mean position (the equilibrium position). Therefore, the total distance covered in one complete cycle (one time period) is twice the amplitude.

### Step 2: Calculate the Distance
1. The particle moves from the mean position (0) to the maximum amplitude position (+A).
2. Then, it moves back to the mean position (0).
3. Next, it moves from the mean position (0) to the negative amplitude position (-A).
4. Finally, it returns to the mean position (0).

Thus, the total distance traveled in one complete cycle is:
\[ \text{Distance} = A + A + A + A = 4A \]

### Step 3: Conclusion
The distance traveled by the particle in one time period is \( 4A \).

### Final Answer:
The distance traveled by the particle in one time period is \( 4A \).

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