The time period of simple harmonic motion depends upon

Options

A. amplitude
B. energy
C. phase constant
D. mass

Explanation

To determine what the time period of simple harmonic motion (SHM) depends upon, we can analyze the formulas associated with SHM.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- SHM is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.

2. **Identifying the Formulas**:
- For a simple pendulum, the time period \( T \) is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.
- For a mass-spring system, the time period \( T \) is given by:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass attached to the spring and \( k \) is the spring constant.

3. **Analyzing the Options**:
- **Amplitude**: The time period does not depend on the amplitude of the oscillation in ideal SHM.
- **Energy**: The energy in SHM is related to the amplitude but does not directly affect the time period.
- **Phase Constant**: The phase constant affects the position of the oscillating object at \( t = 0 \) but does not affect the time period.
- **Mass**: In the case of a mass-spring system, the time period does depend on the mass \( m \).

4. **Conclusion**:
- The time period of simple harmonic motion depends on the mass of the object and the spring constant in the case of a mass-spring system. In the case of a pendulum, it depends on the length of the pendulum and the acceleration due to gravity.

### Final Answer:
The time period of simple harmonic motion depends on the mass (for a mass-spring system) and the length of the pendulum (for a simple pendulum).