Assertion : A particle is under SHM along the x - axis. Its mean position is `x = 2`, amplitude is `A = 2` and angular frequency `omega`. At `t = 0`, particle is at origin, then `x` - co-ordinate versus time equation of the particle will be `x = -2 cos omega t + 2`.
Reason : At `t = 0` , particle is at rest.

Options

A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. Assertion is true, but the Reason is false.
D. Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question regarding the simple harmonic motion (SHM) of a particle.

### Step-by-step Solution:

1. **Understanding the Assertion**:
- The assertion states that a particle is undergoing SHM along the x-axis with a mean position at \( x = 2 \), an amplitude \( A = 2 \), and an angular frequency \( \omega \). At \( t = 0 \), the particle is at the origin \( (x = 0) \).

2. **Formulating the SHM Equation**:
- The general equation for SHM can be expressed as:
\[ x(t) = A \cos(\omega t + \phi) + k \]
where \( k \) is the mean position, \( A \) is the amplitude, and \( \phi \) is the phase constant.
- Here, \( k = 2 \) (mean position) and \( A = 2 \) (amplitude).

3. **Setting Up the Equation**:
- Substituting the values into the SHM equation:
\[ x(t) = 2 \cos(\omega t + \phi) + 2 \]

4. **Finding the Phase Constant**:
- At \( t = 0 \), the particle is at the origin \( (x = 0) \):
\[ 0 = 2 \cos(\phi) + 2 \]
- Rearranging gives:
\[ 2 \cos(\phi) = -2 \implies \cos(\phi) = -1 \]
- This implies \( \phi = \pi \).

5. **Final Equation**:
- Substituting \( \phi = \pi \) back into the equation:
\[ x(t) = 2 \cos(\omega t + \pi) + 2 \]
- Since \( \cos(\theta + \pi) = -\cos(\theta) \), we can rewrite this as:
\[ x(t) = -2 \cos(\omega t) + 2 \]
- This matches the assertion that \( x(t) = -2 \cos(\omega t) + 2 \).

6. **Understanding the Reason**:
- The reason states that at \( t = 0 \), the particle is at rest.
- To check this, we need to find the velocity \( v(t) \):
\[ v(t) = \frac{dx}{dt} = \frac{d}{dt}(-2 \cos(\omega t) + 2) = 2 \omega \sin(\omega t) \]
- At \( t = 0 \):
\[ v(0) = 2 \omega \sin(0) = 0 \]
- This confirms that the particle is at rest at \( t = 0 \).

7. **Conclusion**:
- Both the assertion and the reason are true. However, the reason does not correctly explain the assertion since the assertion is about the position of the particle, while the reason discusses its velocity.

### Final Answer:
- The correct option is **B**: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.