The velocity of a particle performing S.H.M. at extreme position is

Options

A. minimum
B. constant
C. maximum
D. half of the maximum velocity

Answer

To solve the question regarding the velocity of a particle performing Simple Harmonic Motion (S.H.M.) at extreme positions, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Extreme Position**:
- In S.H.M., the extreme positions are the maximum displacements from the mean position (equilibrium position). These positions are denoted as +A and -A, where A is the amplitude of the motion.

**Hint**: Recall that extreme positions correspond to the maximum displacement from the mean position.

2. **Restoring Force at Extreme Position**:
- The restoring force is maximum at these extreme positions. The formula for restoring force is given by \( F = -kx \), where \( x \) is the displacement from the mean position. At extreme positions, \( x \) equals +A or -A, leading to maximum force.

**Hint**: Remember that the restoring force is directly related to displacement in S.H.M.

3. **Velocity Formula in S.H.M.**:
- The velocity \( v \) of a particle in S.H.M. can be expressed as:
\[ v = \omega \sqrt{A^2 - x^2} \]
where \( \omega \) is the angular frequency and \( x \) is the displacement.

**Hint**: Familiarize yourself with the formula for velocity in S.H.M. and the variables involved.

4. **Substituting Extreme Position Values**:
- At the extreme positions, \( x \) is equal to A or -A. Therefore, substituting \( x = A \) or \( x = -A \) into the velocity formula gives:
\[ v = \omega \sqrt{A^2 - A^2} = \omega \sqrt{0} = 0 \]

**Hint**: When substituting extreme position values into the velocity formula, notice how the terms simplify.

5. **Conclusion**:
- The velocity of the particle at the extreme positions (both +A and -A) is zero. This means that at the extreme points, the particle momentarily comes to rest before changing direction.

**Hint**: Think about the physical interpretation of velocity being zero at the points of maximum displacement.

### Final Answer:
The velocity of a particle performing S.H.M. at extreme positions is **0**.