The time period of simple harmonic motion depends upon

Options

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

Explanation

To determine the factors that affect the time period of simple harmonic motion (SHM), we can analyze the relationship between the time period and the parameters involved in SHM.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM):**
- SHM is a type of periodic motion where an object oscillates about an equilibrium position. The motion is characterized by a restoring force proportional to the displacement from the equilibrium position.

2. **Identifying the Parameters:**
- The time period \( T \) of SHM is the time taken for one complete cycle of motion. It is influenced by several factors, including mass and the spring constant.

3. **Using the Formula for Time Period:**
- For a mass \( m \) attached to a spring with spring constant \( k \), the time period \( T \) can be calculated using the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
- Here, \( T \) is the time period, \( m \) is the mass of the object, and \( k \) is the spring constant.

4. **Analyzing the Formula:**
- From the formula, we can see that the time period \( T \) depends on:
- The mass \( m \): As the mass increases, the time period increases.
- The spring constant \( k \): As the spring constant increases, the time period decreases.

5. **Considering Other Options:**
- Amplitude: The amplitude \( A \) does not affect the time period in SHM. It only affects the maximum displacement from the equilibrium position.
- Energy: The total mechanical energy in SHM is related to the amplitude but does not directly affect the time period.
- Phase constant: The phase constant determines the initial position of the oscillating object but does not affect the time period.

6. **Conclusion:**
- Based on the analysis, the time period of simple harmonic motion depends on the mass of the object and the spring constant, but not on amplitude, energy, or phase constant. Therefore, the correct answer is that the time period depends on mass.

### Final Answer:
The time period of simple harmonic motion depends on **mass** (Option 4).