Episode 307: Resonance
Lesson for 16-19
- Activity time 150 minutes
- Level Advanced
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.
- 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.
Student activity: An applet of a forced pendulum
Investigate a virtual pendulum which can be forced.
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.
Student questions: Questions on resonance
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.
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.