# Broomstick pendulum, sinusoidal motion

##### Demonstration

To show that simple harmonic motion (S.H.M.) is sinusoidal.

#### Apparatus and materials

Broomstick pendulum

Paper, roll of

Paint brush

Cathode ray oscilloscope, or PC-based digital oscilloscope

Power supply, 12 V AC

#### Health & Safety and Technical notes

Set up the massive broomstick pendulum as in the diagram (left). Attach to the lower end of the broomstick a paint brush dipped in ink. This will produce an inked line as a roll of paper passes beneath it.

Alternatively, you could make the broomstick pendulum produce a fine line of sand (diagram right). Attach a plastic cup to the broomstick, using a drawing-pin. Fill the cup with fine dry sand. In the bottom of the cup is a hole (2-3 mm diameter) through which the dry sand flows onto the paper, as it is pulled across the floor.

An oscilloscope with a long persistence screen is an advantage but not essential.

#### Procedure

a Set the pendulum swinging and pull the paper steadily across the floor, under the pendulum, so that the brush makes a sinusoidal trace on the paper. (Pull the paper in a direction at right angles to the plane of oscillation.)

Pull the paper faster, to show the sine wave spreads out more, in the same way as the trace on an oscilloscope does when you increase the timebase.

b Use the oscilloscope to demonstrate the waveform of the alternating voltage, first with the timebase switched off and then with the spot running across at constant speed. Compare it with the pendulum trace.

c Increase the speed of the timebase, drawing attention to the way that the waveform changes.

#### Teaching notes

1 Describe the line left by the oscillator as a 'time trace'. The main points of this demonstration are that:

• a simple harmonic motion produces a time trace with a sinusoidal shape
• both the broomstick pendulum and the voltages from AC power supplies are simple harmonic motions
• the shape of the wave produced by a simple harmonic motion will depend on the timebase setting (speed that the paper is pulled)

2 As the broomstick pendulum produces a time trace, point out

• the changing displacement of the pen/cup
• the amplitude of the oscillation (which gradually gets smaller)

Once the time trace is complete, point out that the period (periodic time) remains constant. The frequency (inverse of periodic time) is also constant.

3 You could go on to discuss the fact that isochronous oscillators make good clocks.