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.

Lesson 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 shifted in the right way.

A child on a park swing is the classic example that all can visualise. 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 way that energy is shifted into system must be tuned to the oscillator, or the oscillator must be able to be tuned to the way that energy is being shifted. 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.

Episode 307-1: Barton’s pendulums (Word, 38 KB)

Student activity: An applet of a forced pendulum

Investigate a virtual pendulum which can be forced.

Episode 307-2: Forced oscillations (Word, 20 KB)

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.

Episode 307-3: Book on a string (Word, 41 KB)

Episode 307-4: Resonance of a milk bottle (Word, 91 KB)

Episode 307-5: Resonance of a hacksaw blade (Word, 66 KB)

Episode 307-6: Resonance of a mass on a spring (Word, 98 KB)

Student questions: Questions on resonance

Episode 307-7: Oscillator energy and resonance (Word, 59 KB)

Episode 307-8: Resonance in car suspension systems (Word, 204 KB)

Episode 307-9: Car suspension (Word, 21 KB)

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.

Episode 307-10: Resonance (Word, 47 KB)

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.

Episode 307-11: Tacoma Narrows bridge disaster (Word, 100 KB)

Episode 307-12: Tacoma Narrows: Re-evaluating the evidence (Word, 57 KB)