The force of a particle of mass 1 kg is depends on displacement as F = —4x then the frequency of S.H.M. is

Options

A. `pi Hz`
B. `2pi Hz`
C. `1/pi Hz`
D. `1/(2pi) Hz`

Answer

To solve the problem, we need to find the frequency of the simple harmonic motion (SHM) for a particle of mass 1 kg, given that the force acting on it is \( F = -4x \).

### Step-by-Step Solution:

1. **Identify the Force Equation**:
The force acting on the particle is given by:
\[ F = -4x \]
This is in the form of Hooke's law, which states that \( F = -kx \), where \( k \) is the spring constant.

2. **Determine the Spring Constant \( k \)**:
By comparing the given force equation with the standard form \( F = -kx \), we can identify that:
\[ k = 4 \, \text{N/m} \]

3. **Use the Formula for Time Period \( T \)**:
The time period \( T \) of SHM is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass of the particle and \( k \) is the spring constant.

4. **Substitute the Values**:
Here, the mass \( m = 1 \, \text{kg} \) and \( k = 4 \, \text{N/m} \). Substituting these values into the formula gives:
\[ T = 2\pi \sqrt{\frac{1}{4}} = 2\pi \cdot \frac{1}{2} = \pi \, \text{s} \]

5. **Calculate the Frequency \( f \)**:
The frequency \( f \) is the reciprocal of the time period \( T \):
\[ f = \frac{1}{T} = \frac{1}{\pi} \, \text{Hz} \]

### Final Answer:
The frequency of the simple harmonic motion is:
\[ f = \frac{1}{\pi} \, \text{Hz} \]