The acceleration of a body in SHM is

Options

A. Maximum at the extreme position
B. Maximum at the equilibrium positon
C. Always same
D. Always zero.

Answer

To solve the question regarding the acceleration of a body in Simple Harmonic Motion (SHM), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**: In SHM, the displacement of a body can be described by the equation:
\[ x(t) = A \sin(\omega t + \phi) \]
where \(A\) is the amplitude, \(\omega\) is the angular frequency, and \(\phi\) is the phase constant.

2. **Set Initial Conditions**: For simplicity, we can assume the body starts from the mean position (equilibrium position), which means we can set \(\phi = 0\). Thus, the equation simplifies to:
\[ x(t) = A \sin(\omega t) \]

3. **Calculate Velocity**: The velocity \(v(t)\) is the first derivative of the displacement with respect to time:
\[ v(t) = \frac{dx}{dt} = A \omega \cos(\omega t) \]

4. **Calculate Acceleration**: The acceleration \(a(t)\) is the derivative of the velocity:
\[ a(t) = \frac{dv}{dt} = -A \omega^2 \sin(\omega t) \]

5. **Relate Acceleration to Displacement**: We can express acceleration in terms of displacement:
\[ a(t) = -\omega^2 x(t) \]
This shows that the acceleration is directly proportional to the displacement and acts in the opposite direction.

6. **Determine Maximum Acceleration**: The maximum value of acceleration occurs when the displacement \(x\) is at its maximum value \(A\):
\[ a_{\text{max}} = \omega^2 A \]

7. **Analyze the Options**:
- **Option A**: Maximum at extreme position - **True**. At maximum displacement (extreme position), acceleration is maximum.
- **Option B**: Maximum at equilibrium position - **False**. At equilibrium position (\(x = 0\)), acceleration is zero.
- **Option C**: Always same - **False**. Acceleration varies with displacement.
- **Option D**: Always zero - **False**. Acceleration is not always zero; it varies with position.

8. **Conclusion**: The correct answer is that the acceleration of a body in SHM is maximum at the extreme position.

### Final Answer:
The acceleration of a body in SHM is maximum at the extreme position.

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