A particle executing SHM. The phase difference between acceleration and displacement is

Options

A. 0
B. `pi/2`
C. `pi`
D. `2pi`

Explanation

To find the phase difference between acceleration and displacement for a particle executing Simple Harmonic Motion (SHM), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the equations of SHM**:
The displacement \( x \) of a particle in SHM can be expressed as:
\[ x(t) = A \cos(\omega t) \]
where \( A \) is the amplitude and \( \omega \) is the angular frequency.

2. **Determine the velocity**:
The velocity \( v \) is the time derivative of displacement:
\[ v(t) = \frac{dx}{dt} = -A \omega \sin(\omega t) \]

3. **Determine the acceleration**:
The acceleration \( a \) is the time derivative of velocity:
\[ a(t) = \frac{dv}{dt} = -A \omega^2 \cos(\omega t) \]

4. **Identify the forms of displacement and acceleration**:
From the equations derived:
- Displacement: \( x(t) = A \cos(\omega t) \)
- Acceleration: \( a(t) = -A \omega^2 \cos(\omega t) \)

5. **Analyze the phase of displacement and acceleration**:
The displacement \( x(t) \) is represented by \( \cos(\omega t) \), while the acceleration \( a(t) \) can be rewritten as:
\[ a(t) = -A \omega^2 \cos(\omega t) = A \omega^2 \cos(\omega t + \pi) \]
This indicates that the acceleration is \( \pi \) radians (or 180 degrees) out of phase with the displacement.

6. **Conclusion**:
Therefore, the phase difference between acceleration and displacement is:
\[ \text{Phase difference} = \pi \text{ radians} \]

### Final Answer:
The phase difference between acceleration and displacement in SHM is \( \pi \) radians.

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