Simple pendulum: finding the acceleration due to gravity

Objectives

• Measure the period of a simple pendulum accurately.
• Show that T² is proportional to length.
• Calculate g from the gradient of a graph.

Theory

For small swings the period of a simple pendulum is T = 2π√(L/g). It depends on the length L and on g, but not on the mass of the bob. Squaring gives T² = (4π²/g)·L, so a graph of T² against L is a straight line through the origin with gradient 4π²/g. Timing one swing gives a large percentage error because of reaction time, so time many swings and divide.

T = 2π√(L/g) g = 4π² ÷ gradient of the T²–L graph

Procedure

1. Reduce the release angle to 10° or less.
2. Set the number of oscillations to time to 10 or more.
3. Time the oscillations for one length.
4. Repeat for at least five different lengths.
5. Plot T² against length in the Graph tab and note the gradient.

Precautions

• Keep the release angle small (10° or less).
• Time at least 10 oscillations.
• Count “zero” as the bob is released.

Subject

Physics

Grade

9–11

Chapter

Force and Motion (Nepal National Curriculum (CDC), grade 9)

Difficulty

Medium

Duration

25 min

Safety level

Low

Version

1.0

Apparatus

• Retort stand
• Thread
• Bob
• Metre rule
• Protractor
• Stopwatch