Which of the following statements is correct:

Options

A. In simple harmonic motion, additional potential energy of the once in one time period
B. In simple harmonic motion, constant force have no effect on time period.
C. A block can't perfome SHM, if frictionless force acts on it.
D. Average acceleration in one time period of a SHM is non zero.

Explanation

To solve the question regarding which statement is correct in the context of Simple Harmonic Motion (SHM), we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding SHM**:
- Simple Harmonic Motion is a type of periodic motion where an object moves back and forth around an equilibrium position. The motion is characterized by a restoring force proportional to the displacement from the equilibrium position.

2. **Evaluating Each Statement**:
- **Statement A**: "The additional potential energy in one time period is constant."
- This statement is incorrect. In SHM, potential energy changes as the object moves through its cycle. It is not constant over one time period.

- **Statement B**: "In SHM, a constant force has no effect on the time period."
- This statement is correct. The time period of a particle in SHM depends on the mass of the particle and the spring constant (for a spring system), and it is independent of any constant external force applied to it.

- **Statement C**: "A block can't perform SHM if a frictionless force acts on it."
- This statement is incorrect. A block can perform SHM even in the absence of friction. In fact, friction would hinder SHM rather than facilitate it.

- **Statement D**: "The average acceleration in one time period of SHM is non-zero."
- This statement is incorrect. The average acceleration over one complete cycle of SHM is zero because the acceleration is equal in magnitude and opposite in direction during the two halves of the cycle.

3. **Conclusion**:
- After evaluating all the statements, the correct answer is **Statement B**: "In SHM, a constant force has no effect on the time period."