Assertion : Time period of a spring-block equation of a particle moving along X-axis is x=4+6`"sin"omegat` . Under this situation, motion of particle is not simple harmonic.
Reason : `(d^(2)x)/(dt^(2))` for the given equation is proportional to -x.

Options

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

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the time period of a spring-block equation of a particle moving along the X-axis is given by:
\[ x = 4 + 6 \sin(\omega t) \]
and claims that under this situation, the motion of the particle is not simple harmonic motion (SHM).

2. **Understanding the Reason**:
The reason states that the second derivative of displacement with respect to time, \(\frac{d^2x}{dt^2}\), for the given equation is proportional to \(-x\).

3. **Differentiating the Equation**:
- First, we differentiate \(x\) with respect to time \(t\):
\[ \frac{dx}{dt} = 0 + 6\omega \cos(\omega t) = 6\omega \cos(\omega t) \]
- Next, we differentiate again to find the second derivative:
\[ \frac{d^2x}{dt^2} = -6\omega^2 \sin(\omega t) \]

4. **Relating to Displacement**:
From the original equation, we can express \(\sin(\omega t)\) in terms of \(x\):
\[ 6 \sin(\omega t) = x - 4 \implies \sin(\omega t) = \frac{x - 4}{6} \]
Substituting this back into the second derivative:
\[ \frac{d^2x}{dt^2} = -6\omega^2 \left(\frac{x - 4}{6}\right) = -\omega^2 (x - 4) \]

5. **Identifying the Mean Position**:
The mean position (equilibrium position) of the motion is at \(x = 4\). For simple harmonic motion, the acceleration must be proportional to the negative of the displacement from the mean position.

6. **Conclusion on SHM**:
The expression \(\frac{d^2x}{dt^2} = -\omega^2 (x - 4)\) indicates that the motion is indeed simple harmonic motion about the mean position \(x = 4\).

7. **Evaluating the Assertion and Reason**:
- The assertion that the motion is not SHM is **false**.
- The reason that \(\frac{d^2x}{dt^2}\) is proportional to \(-x\) (with respect to the mean position) is **true**.

### Final Answer:
- **Assertion**: False
- **Reason**: True

The correct option is that the assertion is false and the reason is true.