If the period of oscillation of particle performing simple harmonic motion is 8 s, than the frequency of its kinetic energy will be

Options

A. `0.5 s^(-1)`
B. `0.25s^(-1)`
C. `1s^(-1)`
D. `2 s^(-1)`

Answer

To find the frequency of the kinetic energy of a particle performing simple harmonic motion (SHM) when the period of oscillation is given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The period of oscillation \( T \) is given as \( 8 \) seconds.

2. **Calculate the Frequency of Oscillation:**
- The frequency \( f \) of oscillation is related to the period \( T \) by the formula:
\[ f = \frac{1}{T} \]
- Substituting the given period:
\[ f = \frac{1}{8 \text{ s}} = 0.125 \text{ Hz} \]

3. **Determine the Frequency of Kinetic Energy:**
- The frequency of kinetic energy in SHM is twice the frequency of oscillation. Therefore:
\[ f_{\text{KE}} = 2 \times f \]
- Substituting the frequency of oscillation:
\[ f_{\text{KE}} = 2 \times 0.125 \text{ Hz} = 0.25 \text{ Hz} \]

4. **Final Result:**
- The frequency of the kinetic energy is:
\[ f_{\text{KE}} = 0.25 \text{ Hz} \]

### Summary:
The frequency of the kinetic energy of the particle performing simple harmonic motion is \( 0.25 \text{ Hz} \).