Time period of a simple pendulum only depends on the _______________ of the string.

Options

A. Oscillation
B. frequency
C. length
D. amplitude

Answer

To solve the question regarding what the time period of a simple pendulum depends on, we can follow these steps:

### Step 1: Understand the Concept of Time Period
The time period of a pendulum is defined as the time taken to complete one full oscillation. This means the time it takes for the pendulum to swing from its starting position to the maximum displacement on one side, back through the mean position, and then to the maximum displacement on the other side, and finally return to the starting position.

**Hint:** Remember that the time period is related to the motion of the pendulum and how long it takes to complete one full cycle.

### Step 2: Identify the Factors Affecting Time Period
The time period of a simple pendulum is influenced by several factors, including:
- Length of the string (L)
- Acceleration due to gravity (g)
- Amplitude of the swing (which is generally small for a simple pendulum)

However, for small angles of oscillation, the amplitude does not significantly affect the time period.

**Hint:** Consider which of these factors remains constant and which one varies when you change the pendulum's setup.

### Step 3: Use the Formula for Time Period
The formula for the time period (T) of a simple pendulum is given by:

\[ T = 2\pi \sqrt{\frac{L}{g}} \]

Where:
- \( T \) is the time period,
- \( L \) is the length of the string,
- \( g \) is the acceleration due to gravity.

From this formula, we can see that the time period is directly related to the length of the string (L) and is independent of the mass of the bob and the amplitude of the swing (as long as the amplitude is small).

**Hint:** Focus on the variable in the formula that directly affects the time period.

### Step 4: Conclusion
From the analysis and the formula, we conclude that the time period of a simple pendulum only depends on the **length of the string**.

**Final Answer:** The time period of a simple pendulum only depends on the **length** of the string.

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