### Episode 307: Resonance

Simple harmonic oscillators show resonance if they are forced to vibrate at their natural frequency. This is a phenomenon of great importance in many aspects of science.

Summary

• Discussion: Resonance as a phenomenon. (10 minutes)
• Demonstration: Barton’s pendulums. (10 minutes)
• Student activity: An applet of a forced pendulum. (20 minutes)
• Student experiment: A selection of model systems. (30 minutes)
• Student questions: Questions on resonance. (40 minutes)
• Discussion: The effect of damping on resonance. (10 minutes)
• Demonstration and student reading: The Tacoma Narrows bridge disaster. (30 minutes)

Discussion: Resonance as a phenomenon
An oscillator can be forced to vibrate with increasing amplitude; to do this; energy must be supplied in the right way.

A child on a park swing is the classic example that all can visualize. The push must come at the same natural frequency as the oscillating pendulum-like swing and at the right point in the swing’s cycle.

So the energy input system must be ‘tuned’ to the oscillator, or the oscillator must be able to be tuned to the available energy input. Matching up the natural frequency and the forcing frequency results in a resonant system. The fundamental resonant frequency is synonymous with the natural frequency of an oscillator.

Resonance can lead to very large oscillation amplitudes that can result in damage. E.g. buildings etc need to have their natural frequency very different from the likely vibration frequencies due to earthquakes.

Demonstration: Barton’s pendulums
Barton’s pendulums are a famous demonstration of a resonance effect.

TAP 307-1: Barton’s pendulums

Student activity: An applet of a forced pendulum
Investigate a virtual pendulum which can be forced.

monet.physik.unibas.ch/~elmer/pendulum

TAP 307-2: Forced oscillations

Student experiment: A selection of model systems
Students can be allocated to one of the following experiments (duplication is easy), followed by a brief plenary session where each system is demonstrated to the whole class.

TAP 307-3: Book on a string

TAP 307-4: Resonance of a milk bottle

TAP 307-5: Resonance of a hacksaw blade

TAP 307-6: Resonance of a mass on a spring

Student questions: Questions on resonance

TAP 307-7: Oscillator energy and resonance

TAP 307-8: Resonance in car suspension systems

TAP 307-9: Car suspension

Discussion: The effect of damping on resonance
If a resonant system is forced at frequencies above or below the resonant (natural) frequency f0, the amplitude of oscillation will be reduced. The ‘resonance curve’ peaks at f0. You may need to discuss how the shape of the curve depends on the degree of damping.

TAP 307-10: Resonance

Demonstration and student reading: The Tacoma Narrows bridge disaster.
The Tacoma Narrows bridge disaster is generally described as a consequence of resonance. However, the full details of the mechanism are still debated. If possible show a video of the bridge as it collapsed in high winds on 7 November 1940. However, it seems more than likely that it is an example of positive feedback, a sort of “inverse damping” which created this effect.

TAP 307-11: Tacoma Narrows bridge disaster

TAP 307-12: Tacoma Narrows: Re-evaluating the evidence