1. Introduction

A simple pendulum is a weight (or bob) suspended from a pivot so it can swing freely back and forth. It is one of the classic examples of simple harmonic motion in physics.

Definition of Key Terms:

• Amplitude: The maximum angle (in degrees) the pendulum is displaced from the vertical before release.
• Time Period (T): The time taken for the pendulum to complete one full swing (to and fro motion).
• Oscillation: One complete cycle of movement from one extreme to another and back.

According to the theory, for small angles (less than 15°), the amplitude does not affect the time period of the pendulum. This practical is aimed at confirming that statement.

2. Objective

To investigate whether the amplitude (angle of swing) affects the time period of a pendulum.

3. Apparatus

• Clamp stand and retort stand
• Thread or light string (~1 meter long)
• Metal bob (or heavy small object)
• Protractor
• Stopwatch
• Ruler or meter rule

4. Procedure

1. Set up the pendulum by tying the bob to the string and fixing the string to the stand.
2. Ensure the length of the string is constant throughout the experiment (e.g. 70 cm).
3. Use a protractor to pull the bob to an amplitude of 5° and release it without pushing.
4. Use a stopwatch to measure the time for 10 oscillations. Record the time.
5. Repeat the same procedure for amplitudes of 10°, 15°, and 20°.
6. Calculate the time period for each trial using: T = Time for 10 oscillations / 10

5. Observation Table

Amplitude (°)	Time for 10 Oscillations (s)	Time Period T (s)
5	19.8	1.98
10	19.9	1.99
15	20.0	2.00
20	20.1	2.01

6. Graph

7. Results and Analysis

From the results and graph above, it is clear that as amplitude increases from 5° to 20°, the time period changes only slightly. This change is too small to be considered significant.

This confirms the theoretical prediction that for small amplitudes, the time period of a pendulum is independent of the amplitude.

8. Conclusion

The time period of a simple pendulum is not affected by small changes in amplitude. Therefore, amplitude has negligible effect on the period of a pendulum for small angular displacements (usually less than 15°).

9. Solved NECTA-style Questions

Question 1:

A student swings a pendulum at amplitudes of 5°, 10°, 15°, and 20° and records the time for 10 oscillations as follows: 19.8s, 19.9s, 20.0s, and 20.1s. What conclusion can be drawn about the effect of amplitude on the time period?

Solution: Calculating T:

• 5°: T = 19.8 / 10 = 1.98s
• 10°: T = 19.9 / 10 = 1.99s
• 15°: T = 20.0 / 10 = 2.00s
• 20°: T = 20.1 / 10 = 2.01s

Since the time period remains almost the same, the conclusion is that amplitude has negligible effect on the time period of the pendulum.

Question 2:

Why is it recommended to use small amplitudes (less than 15°) in pendulum experiments?

Answer: Because the standard formula T = 2π√(L/g) assumes simple harmonic motion which is only accurate for small amplitudes. At larger angles, the motion becomes non-linear and time period slightly increases.

10. NECTA Exam References

NECTA 2018

Task: Investigate how amplitude affects the pendulum's time period and plot a graph. What do you conclude?

Answer: Graph shows horizontal line. Time period remains constant. Conclusion: Amplitude has no significant effect.

NECTA 2021

Task: Measure time for 10 oscillations at varying amplitudes. What does the graph suggest?

Answer: Time period stays the same. Confirm independence of time period on amplitude (for small angles).

11. Practical Tips

• Ensure minimal air resistance by using a smooth, heavy bob.
• Measure time over 10 oscillations for better accuracy.
• Always release the pendulum gently without pushing it.
• Keep the swing small to follow the assumptions of SHM.