The phase of a particle in S.H.M. is `pi//2`, then :

Options

A. Its velocity will be maximum
B. Its acceleration will be minimum
C. Restoring force on it will be minimum.
D. Its displacement will be maximum.

Answer

To solve the question regarding the phase of a particle in Simple Harmonic Motion (S.H.M.) being \( \frac{\pi}{2} \), we need to analyze the implications of this phase on the particle's displacement, velocity, acceleration, and force.

### Step-by-Step Solution:

1. **Understanding Phase in S.H.M.**:
- The phase \( \phi \) in S.H.M. determines the position of the particle in its oscillatory motion. The general equations for displacement \( x \), velocity \( v \), and acceleration \( a \) in S.H.M. are:
- Displacement: \( x(t) = A \cos(\omega t + \phi) \)
- Velocity: \( v(t) = -A \omega \sin(\omega t + \phi) \)
- Acceleration: \( a(t) = -A \omega^2 \cos(\omega t + \phi) \)
- Here, \( A \) is the amplitude, \( \omega \) is the angular frequency, and \( \phi \) is the phase.

2. **Substituting the Phase**:
- Given that the phase \( \phi = \frac{\pi}{2} \):
- Displacement:
\[ x = A \cos\left(\frac{\pi}{2}\right) = A \cdot 0 = 0 \]
- Velocity:
\[ v = -A \omega \sin\left(\frac{\pi}{2}\right) = -A \omega \cdot 1 = -A \omega \]
- Acceleration:
\[ a = -A \omega^2 \cos\left(\frac{\pi}{2}\right) = -A \omega^2 \cdot 0 = 0 \]

3. **Analyzing the Results**:
- From the calculations:
- Displacement \( x = 0 \)
- Velocity \( v = -A \omega \) (which is maximum in magnitude)
- Acceleration \( a = 0 \)
- The restoring force \( F \) is related to acceleration by \( F = ma \). Since \( a = 0 \), the force is also zero.

4. **Conclusion**:
- The results indicate:
- **Displacement** is at its minimum (0).
- **Velocity** is at its maximum (in magnitude).
- **Acceleration** is at its minimum (0).
- **Restoring Force** is also at its minimum (0).

### Final Answer:
- Displacement is minimum, velocity is maximum, acceleration is minimum, and restoring force is minimum when the phase of the particle in S.H.M. is \( \frac{\pi}{2} \).