# Episode 304: Simple pendulum

Lesson for 16-19

- Activity time 120 minutes
- Level Advanced

This episode reinforces many of the fundamental ideas about simple harmonic motion (SHM).

Lesson Summary

- Student experiment: Measuring the restoring force (20 minutes)
- Student experiment: Testing the relationship
- Student activity: Using an applet of a pendulum (30 minutes)
- Discussion: Gravitational and inertial mass (10 minutes)
- Student questions: Calculations involving pendulums (30 minutes)

*T*= 2 π

*l*

*g*(30 minutes)

Note a complication: a simple pendulum shows SHM only for small amplitude oscillations.

## Student experiment: Measuring the restoring force

Measure the restoring force for a simple pendulum.

Episode 304-1: The simple pendulum (Word, 57 KB)

## Student experiment: Testing the relationship

Test the relationship *T* = 2 π *l* *g* for a simple pendulum. Students could decide for themselves which measurements to make, which quantities to vary, and how to process and interpret the results. Encourage them to look for deviations from linear behaviour, arising from large-amplitude oscillations.

## Student activity: Using an applet of a pendulum

Investigate a virtual pendulum; this allows you to vary *g* . You can also force the pendulum, which is useful later when studying resonance.

NB: the analysis of the data uses log-log plots, so this may not be suitable for all students.

Episode 304-2: Virtual pendulum (Word, 31 KB)

## Discussion: Gravitational and inertial mass

The fact that the period of a simple pendulum is independent of the mass of the bob is an example of the Principle of Equivalence – something still not understood today and being tested by very sophisticated experiments involving astronomical measurements on the one hand and how single atoms fall due to gravity on the other.

The basic puzzle is why the *m* in *F**m* = *a* (where *m* is the inertial mass which determines how an object responds to any unbalanced force) has exactly the same magnitude as the *m* in *m**g* (where the *m* is the gravitational mass, the source of the gravitational force).

In deriving the equation for the period of a simple pendulum, we have used both, and used the fact that numerically they cancel out.

## Student questions: Calculations involving pendulums

These questions reinforce basic ideas about SHM.

Episode 304-3: Pendulum (Word, 25 KB)