Resonance of a pendulum

Class experiment

In this experiment the amplitude of forced vibrations is measured as the driving frequency varies. It could be used as part of a circus of experiments for students.

Apparatus and Materials

• Resonance kit, as shown in the diagram
• Metre rule
• Retort stand base, rod, boss, and clamp
• Stopclock
• Card
• Adhesive tape

Health & Safety and Technical Notes

Set the apparatus up in advance. The two strips are lock-nutted together about 20 cm from the top of the vertical strip. The solder is bent as shown, so that it is supported by the horizontal strip but free to swing. (Coiled solder is easily bent onto the required shape.) The horizontal strip rests on the open jaws of a clamp, which acts as a pivot.

Read our standard health & safety guidance

Procedure

1. The pendulum of solder is the driven oscillator. The driving force is provided by the horizontal strip. Its frequency can be varied by moving the adjustable mass up or down. The amplitude of vibration can be measured using the mm scale fixed on the bench.
2. A damping vane made of paper may be attached to the solder with adhesive tape.
3. Vary the frequency of the driving force while measuring the amplitude of vibration of the V-shaped solder. Keep the oscillations of the driver gentle.
4. Plot a graph of amplitude of the forced vibrations v driving force.
5. Fix the card to the solder and then repeat the same experiment.

Teaching Notes

• It should be possible for students to measure the amplitude of forced vibrations  over a range of frequencies for both lightly damped and heavily damped vibrations. In systems that are too lightly damped, transient vibrations are persistent and can cause confusion.
• Students can also be asked to closely observe the phase relationship between the oscillations of the driver and the solder, across the range of driving frequencies, with and without damping.
• Adequate time is essential. A single long practical session may not be enough.

This experiment has yet to undergo a health and safety check.