Assertion : In x=3+4 `"cos" omegat` , amplitude of oscillation is 4 units.
Reason : Mean position is at x=3.

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 1: Understanding the Assertion
The assertion states that in the equation \( x = 3 + 4 \cos(\omega t) \), the amplitude of oscillation is 4 units.

**Explanation**:
In a simple harmonic motion (SHM), the general form of the equation is:
\[ x = A \cos(\omega t + \phi) \]
where \( A \) is the amplitude. In the given equation, \( x = 3 + 4 \cos(\omega t) \), we can see that the term \( 4 \) is the coefficient of the cosine function, which represents the amplitude. Therefore, the amplitude is indeed 4 units.

### Step 2: Understanding the Reason
The reason states that the mean position is at \( x = 3 \).

**Explanation**:
In the equation \( x = 3 + 4 \cos(\omega t) \), the mean position (or equilibrium position) is the value of \( x \) when the cosine function is zero (i.e., when \( \cos(\omega t) = 0 \)). This occurs when:
\[ x = 3 + 4 \cdot 0 = 3 \]
Thus, the mean position is indeed at \( x = 3 \).

### Step 3: Conclusion
Both the assertion and the reason are correct:
- The amplitude of oscillation is 4 units (Assertion is true).
- The mean position is at \( x = 3 \) (Reason is true).

However, the reason does not explain the assertion directly; it simply states a fact about the mean position without linking it to the amplitude.

### Final Answer
Both the assertion and reason are correct, but the reason is not the correct explanation for the assertion. Therefore, the correct option is that both assertion and reason are correct, but the reason does not explain the assertion.

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