If time of mean position from amplitude (extreme) position is 6 s. then the frequency of SHM will be :

Options

A. 0.01 Hz
B. 0.02 Hz
C. 0.03 Hz
D. 0.04 Hz

Explanation

To find the frequency of Simple Harmonic Motion (SHM) given that the time from the mean position to the extreme position is 6 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Motion**: In SHM, the motion can be visualized as oscillating between two extreme positions (amplitudes) and passing through a mean position. The time taken to move from one extreme position to the mean position is a quarter of the total time period (T) of the motion.

2. **Setting Up the Equation**: Given that the time from the mean position to the extreme position is 6 seconds, we can denote this time as \( t/4 \), where \( t \) is the total time period of the motion. Thus, we have:
\[ \frac{t}{4} = 6 \text{ seconds} \]

3. **Calculating the Total Time Period (T)**: To find the total time period \( t \), we can rearrange the equation:
\[ t = 6 \times 4 = 24 \text{ seconds} \]

4. **Finding the Frequency (f)**: The frequency \( f \) of SHM is defined as the reciprocal of the time period:
\[ f = \frac{1}{t} \]
Substituting the value of \( t \):
\[ f = \frac{1}{24} \text{ Hz} \]

5. **Calculating the Frequency**: Performing the calculation:
\[ f = 0.04167 \text{ Hz} \approx 0.04 \text{ Hz} \]

### Final Answer:
The frequency of SHM is approximately **0.04 Hz**.

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