Damped and Coupled Oscillations - extension material

A damped oscillator is... zLosing energy zrun the following spreadsheet to see thisrun the following spreadsheet to see this zdamping can be: yunderdamped yoverdamped ycritically damped

Coupled Oscillations... zSometimes 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

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

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

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

Wave speed... zThe speed of a wave is NOT the same as the speed with which parts of the propagating medium move! zFor mechanical waves we can show that  where T is the tension of the medium and  is the density.

Wave Pulses and Superposition zWaves 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

Wave phase... zThe 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

Wave reflection, phase and the influence of the medium... zWhen 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: ywhen a wave passes from a rare medium to a dense medium the reflected wave travels back with its phase inverted (flipped by 180 o ) ywhen a wave travels from a dense medium to a rare medium NO PHASE inversion occurs