## Abstract

This experiment aims to investigate the relationship between the length of a simple pendulum and the time period of oscillation. By varying the length of the pendulum and measuring the corresponding time periods, the acceleration due to gravity (g) can be calculated.

## Introduction

A simple pendulum consists of a mass (bob) suspended from a fixed point (pivot) by a string or rod. The time period of a pendulum's oscillation depends on its length and the acceleration due to gravity (g). This experiment explores this relationship and aims to calculate the value of g.

## Procedure

- Set up a simple pendulum by suspending a bob from a fixed support.
- Measure the length (\( L \)) of the pendulum from the point of suspension to the center of the bob.
- Displace the pendulum to a small angle and release it.
- Measure the time (\( T \)) taken for a certain number of oscillations (\( n \)).
- Repeat the experiment for different lengths of the pendulum.

## Observations and Calculations

Assume the following observations were made during the experiment:

- Length of pendulum (\( L \)): 50 cm
- Time for 10 oscillations (\( T \)): 12.6 seconds
- Number of oscillations (\( n \)): 10

The time period (\( T \)) of one oscillation can be calculated using the formula:

**\( T = \frac{{\text{Total time}}}{{\text{Number of oscillations}}} \)**

The acceleration due to gravity (\( g \)) can be calculated using the formula:

**\( g = \frac{{4\pi^2 \cdot L}}{{T^2}} \)**

## Conclusion

The experiment demonstrates the inverse relationship between the length of a simple pendulum and its time period of oscillation. By analyzing these relationships, the value of the acceleration due to gravity (g) can be accurately calculated.

## Short Questions with Answers

- What is a simple pendulum?

Answer: A mass suspended from a fixed point by a string or rod. - What factors affect the time period of a pendulum?

Answer: Length of the pendulum and acceleration due to gravity. - What is the formula for calculating the time period of a pendulum?

Answer: \( T = \frac{{2\pi \cdot \sqrt{L}}}{g} \) - What is the relationship between pendulum length and time period?

Answer: As pendulum length increases, time period increases. - How does changing the length of the pendulum affect the value of g?

Answer: It allows calculation of g using the formula \( g = \frac{{4\pi^2 \cdot L}}{{T^2}} \). - What is the SI unit of length?

Answer: Meter (m). - What is the SI unit of time?

Answer: Second (s). - What precautions should be taken during the experiment?

Answer: Ensure accurate measurements, minimize air resistance, and use a stable support for the pendulum. - Why is it important to measure the time for multiple oscillations?

Answer: To reduce timing errors and obtain a more accurate average time. - What is the purpose of displacing the pendulum to a small angle?

Answer: To ensure simple harmonic motion and accurate results. - What is the value of pi (\( \pi \))? Answer: Approximately 3.14159.
- How does the amplitude of oscillation affect the time period?

Answer: It does not affect the time period significantly for small angles of oscillation. - What is the period of a pendulum?

Answer: The time taken for one complete oscillation. - What is the relationship between the period and frequency of oscillation?

Answer: They are inversely proportional: \( T = \frac{1}{f} \). - Why is it important to repeat the experiment for different lengths of the pendulum?

Answer: To verify the relationship between pendulum length and time period and to minimize experimental errors. - What factors might affect the accuracy of the experiment?

Answer: Air resistance, friction at the pivot point, and variations in gravitational acceleration at different locations. - How can the accuracy of timing measurements be improved?

Answer: Using a stopwatch with high precision and repeating the timing for multiple oscillations to calculate the average time. - What is the significance of using a rigid support for the pendulum?

Answer: It ensures that the pendulum oscillates along a fixed path without unnecessary movement or wobbling. - What is the effect of increasing the length of the pendulum?

Increasing the length of the pendulum increases the time period of oscillation. - How does the value of g vary with location?

Answer: The value of g varies slightly with location due to differences in gravitational acceleration at different places on Earth. - What is the relationship between the period of oscillation and the square root of the length of the pendulum?

Answer: The period of oscillation is directly proportional to the square root of the length of the pendulum.

## MCQs with Answers

- What is the purpose of varying the length of the pendulum in the experiment?
- To test the effect of temperature on pendulum oscillation
- To study the effect of length on the time period of the pendulum
- To measure the impact of surface friction on pendulum motion
- To observe the influence of pendulum material on time period

**Answer: B. To study the effect of length on the time period of the pendulum** - What happens to the time period of a pendulum if its length is doubled, assuming all other factors remain constant?
- It becomes four times larger
- It remains the same
- It becomes half
- It becomes twice as large

**Answer: D. It becomes twice as large** - How does increasing the length of a pendulum affect its frequency of oscillation?
- It decreases the frequency
- It increases the frequency
- It has no effect on the frequency
- It makes the frequency unpredictable

**Answer: A. It decreases the frequency** - What factor is primarily responsible for the time period of a pendulum?
- Mass of the pendulum
- Length of the pendulum
- Surface area of the pendulum
- Material of the pendulum

**Answer: B. Length of the pendulum** - How does the value of acceleration due to gravity (g) affect the time period of a pendulum?
- It has no effect on the time period
- It increases the time period
- It decreases the time period
- It makes the time period unpredictable

**Answer: B. It increases the time period**