10.7 Damped and Driven Oscillations

Simple harmonic oscillators that we encounter in the real world do not oscillate forever. Unlike the Energizer Bunny, they do not keep going and going. There is usually some friction present and that friction causes the motion to become smaller and smaller or to decay or to die out or to damp out. "Damped" simply means gradually decreasing.

Figure 10.12 The amplitude of a mass oscillating under

water gets smaller or decays as time goes on. This is a

damped harmonic oscillator.

Animation or video. No interactivity needed.

Springs on an automobile turn the car into a harmonic oscillator. Shock absorbers turn it into a damped harmonic oscillator and keep it from continuing to bounce up and down after every bump or pot hole a tire encounters. Shock absorbers designed for a lightweight sports car would not provide enough damping for a heavy van and would allow several oscillations after each bounce. Likewise, shock absorbers designed for a heavy pickup would provide too much damping for a small sports coupe and would give a stiff, uncomfortable ride. Shock absorbers must be designed with the mass of the car and the stiffness of the springs taken into account.

If you give only little pushes to an oscillator-but ensure that those pushes come at just the right time-you can still give the oscillator a very large amplitude. A fine example of this is pushing someone on a playground swing. If you give just a small push, but give it at the right time, your friend can still end up swinging very high. This is an example of resonance of a driven harmonic oscillator. If forces from the outside are given at the resonance frequency of the oscillator, the resulting amplitude may be quite large.

Consider the two matched chime boxes. If you strike one of the chimes it will sound, causing the air to vibrate with the same frequency as the chime. Now touch that chime and stop it from sounding. You will hear that the other chime is now sounding-just because the air around it was vibrating at its resonance frequency!

The second chime is being driven by the air at its resonance frequency. This resonance frequency is also sometime called the natural frequency of the oscillator.

Figure 10.13 Striking a chime will cause it to sound or vibrate. The sound

produced by that chime will then cause the other chime to sound

because the air vibrates at the resonance frequency of that chime and drives the chime.

Video instead of photo here.

Here is another interesting example of resonance. Just as the vibration of air at the right frequency causes the chime to oscillate or ring, vibration of air at the right frequency will cause a glass to oscillate or ring. If this oscillation can be made great enough, the oscillating glass will break.

This is another example of resonance.

(Sanny & Moeb, p 292)

Figure 10.14 A glass can be broken by a sound if that

sound is at the resonance frequency of the glass.

Q: What does damping have to do with the devices that close doors?

A: First consider the simplest door-closer, a spring attached to a screen door. Basically, this is a simple harmonic oscillator without damping. That means the door will be traveling its fastest as it goes through its equilibrium position-the door jamb. Wham! Adding some mechanism with damping means the door will slow down as it approaches the door jamb. If the damping is too great, the door will come shut very slowly and heated or cooled air will come out and insects will come in; this is called overdamping. If the damping is too little, the door will come shut faster but still hit the door jamb with a thud; this is underdamping. When adjusted right, the door will come shut rapidly yet settle into the door jamb as it comes to rest; this is critical damping.