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WAVES

RESONANCE and NATURAL FREQUENCIES

DAMPED OSCILLATIONS

For a damped oscillating system, the total energy decreases with time,

FORCED (DRIVEN) OSCILLATIONS and RESONANCE

If we displace an object suspended by a spring from equilibrium and let it go it oscillates at its natural frequency

mass of object spring constant

Driven (force) oscillations: if a periodic force at another frequency is applied, the system will vibrate at the driving frequency. Forced oscillations are small unless the driving frequency is close to the natural frequency.

When the driving frequency is close to the natural frequency, the oscillations can be large - this is called resonance. Away from resonance, energy transfer to the oscillations is inefficient. At resonance, there is efficient transfer which may cause an oscillating system to fail.

Why did marching soldiers break-step in crossing a bridge?

Wine glass experiment YouTube video

Chladni Plates YouTube video

The driving force generates travelling waves in the system. At a natural frequency of vibration the travelling waves interfere with each producing standing waves which are characterized by antinodes (regions of large amplitude vibrations) and nodes (regions of very small amplitude vibrations).

Do a web search on Amazing Resonance Experiments

Resonance phenomena occur widely in natural and in technological applications:

Emission & absorption of light / Lasers / Tuning of radio and television sets / Mobile phones / Microwave communications / Machine, building and bridge design /

Musical instruments / Medicine (magnetic resonance imaging)

Self-excited oscillations

Sometimes steady forces can cause large oscillations at the natural frequency.

Do a web search for videos on playing music with wine glasses.

Do a web search for videos on Tacoma Narrows Bridge collapse.

When a system is excited by a driving force, the system will vibrate at the frequency of the driving force. When the damping is small and the driving frequency is close to a natural frequency of vibration of the system, the amplitude of the vibration can be very large (and often dramatic). This phenomenon is called resonance. The natural frequency of a system is called its resonant frequency.

Why can buildings collapse during an earthquake ?

The ground vibrates due the surface waves generated by an earthquake causing a building to rock back and forth and up and down.

VISUAL PHYSICS ONLINE

If you have any feedback, comments, suggestions or corrections please email:

Ian Cooper School of Physics University of Sydney

ian.cooper@sydney.edu.au