A particle executes SHM with frequency 4 Hz. Frequency with which its PE oscillates is

Options

A. 4 Hz
B. 2 Hz
C. 6 Hz
D. 8 Hz

Answer

To find the frequency with which the potential energy (PE) oscillates for a particle executing simple harmonic motion (SHM) with a given frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the frequency of SHM**:
The frequency of the particle executing SHM is given as \( f = 4 \, \text{Hz} \).

2. **Understand the relationship between potential energy and SHM**:
In SHM, the potential energy oscillates between zero at the mean position and maximum at the extreme positions. The potential energy reaches its maximum when the particle is at the extreme positions and is zero when the particle is at the mean position.

3. **Determine the oscillation of potential energy**:
The potential energy oscillates with a frequency that is related to the frequency of the SHM. Specifically, the potential energy oscillates twice for every complete oscillation of the particle. This is because the potential energy goes from zero to maximum and back to zero during the first half of the oscillation and then goes from zero to maximum and back to zero again during the second half.

4. **Calculate the frequency of potential energy**:
Since the potential energy oscillates twice for each complete oscillation of the particle, the frequency of the potential energy \( f_{PE} \) can be calculated as:
\[ f_{PE} = 2 \times f \]
Substituting the value of \( f \):
\[ f_{PE} = 2 \times 4 \, \text{Hz} = 8 \, \text{Hz} \]

5. **Conclusion**:
The frequency with which the potential energy oscillates is \( 8 \, \text{Hz} \).

### Final Answer:
The frequency with which the potential energy oscillates is \( 8 \, \text{Hz} \).

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