`F - x` equation of a body of mass `2kg` in SHM is
`F + 8x = 0`
Here, `F` is in newton and `x` in meter.Find time period of oscillations.

Explanation

To solve the problem, we need to analyze the given equation of motion for a body in simple harmonic motion (SHM) and find the time period of oscillations.

### Step-by-Step Solution:

1. **Identify the given equation**:
The force equation is given as:
\[ F + 8x = 0 \]
Rearranging this, we can express the force \( F \) as:
\[ F = -8x \]

2. **Relate force to mass and acceleration**:
According to Newton's second law, force can also be expressed as:
\[ F = m \cdot a \]
where \( m \) is the mass and \( a \) is the acceleration. Given that the mass \( m = 2 \, \text{kg} \), we can write:
\[ -8x = 2a \]

3. **Express acceleration in terms of displacement**:
From the above equation, we can express acceleration \( a \) as:
\[ a = \frac{-8x}{2} = -4x \]

4. **Relate acceleration to SHM**:
In SHM, the acceleration can also be expressed as:
\[ a = -\omega^2 x \]
where \( \omega \) is the angular frequency. Setting the two expressions for acceleration equal gives us:
\[ -4x = -\omega^2 x \]

5. **Solve for angular frequency \( \omega \)**:
Since \( x \) is not zero, we can divide both sides by \( x \):
\[ \omega^2 = 4 \]
Taking the square root, we find:
\[ \omega = 2 \, \text{radians/second} \]

6. **Calculate the time period \( T \)**:
The time period \( T \) of oscillation is related to the angular frequency \( \omega \) by the formula:
\[ T = \frac{2\pi}{\omega} \]
Substituting the value of \( \omega \):
\[ T = \frac{2\pi}{2} = \pi \, \text{seconds} \]

### Final Answer:
The time period of oscillations is \( T = \pi \, \text{seconds} \).