1. Damped and Coupled Oscillations - extension material
Vibration in the
real world

2. A damped oscillator is... Losing energy
run the following spreadsheet to see this
damping can be:
underdamped
overdamped
critically damped

3. Coupled Oscillations...
Sometimes an object vibrates in a number of different ways and at different frequencies. Sometimes these vibrations can interact - we call this a coupled oscillation
coupled pendula
coupled springs
longitudinal & torsional coupling

4. Resonance and Resonant Coupling...
What happens if you “jiggle” a system (maybe a spring-mass) at the same rate that it naturally vibrates?
What if coupled oscillators have matching frequencies?
Resonance is the condition that occurs when we drive a system (by coupling or other means) at one of its natural frequencies.

5. Wave Motion in General
Wave motion is one of “nature’s” most common ways of transporting energy.
Mechanical waves propagate through a medium
Three basic flavours:
transverse
longitudinal
torsional
go to this applet to illustrate this...

6. Wave Equation
Wavelength (crest-crest or trough-trough distance), frequency and wave speed are related in a very simple way:
“lambda” = wavelength
Wave speed
frequency

7. Wave speed...
The speed of a wave is NOT the same as the speed with which parts of the propagating medium move!
For mechanical waves we can show that
where T is the tension of the medium and r is the density.

8. Wave Pulses and Superposition
Waves and wave pulses add together! This is a very important property and the Principle of Superposition is vital to our understanding of wave phenomena.
Go to a Maple Worksheet illustrating this
Go to an Applet that illustrates this

9. Wave phase...
The idea of wave phase relates the position of the crest (or any other point) on one wave to the same point on another wave. If these points match then the waves are “in phase”, otherwise we talk about a phase difference between the waves.
go to this applet to see this

10. Wave reflection, phase and the influence of the medium...
When waves encounter a change in media there is always transmission and reflection at the interface. We can easily show this (and will) and you will see that:
when a wave passes from a rare medium to a dense medium the reflected wave travels back with its phase inverted (flipped by 180o)
when a wave travels from a dense medium to a rare medium NO PHASE inversion occurs