eulers formulae

Complex harmonic motion

Complex harmonic motion occurs when a number of simple harmonic motions are combined.

Chords in music are an example of this phenomenon.

Forced Damped Harmonic Motion is another term for Complex Harmonic motion.

Chords on a guitar is also valid as air stops the vibration of the strings and and they do interact with each other passing energy by air to each other however that is a difficult scenario to think about if you do not understand real world CHM.

A good example of which is the suspension on a car. Assume one wheel.

The spring is the element which provides the simple harmonic motion and without external inflences would oscilate as a standard spring, assuming no heating losses internal to itself or deformation of the spring took place.

The damping is the shock absorber in the system this limits the ability of the spring to oscilate and as the name suggests damps or tries to stop the spring from moving in the simple harmonic motion expected in a predictable manner in the system suggested. The damper (or shock absorber) dissapates energy by mechanical transfer of energy to a fluid normally oil that heats up as a result of its viscoscity opposing motion through a series of valves to restict flow around a circuit. The energy is absorbed by the fluid and and then transfered by radiation and convection to the air passing over the shock absorber or in extreme cases the oil vents to the atmosphere.

The force exherted that is the forced element of the system is the bumps in the road to which the suspension system has to respond that is every pothole that is driven over that excites the system, this is the forced part of the equation.

So Forced Damped Simple Harmonic Motion.

The shock absorber traditionally is simple and not controlled but that is becoming more refined. Control Theory should now be looked into if you are interested. And if you can integrate electronics with it talk to (traditionally) lotus or any F1 car company if you can do it non electronically.

It starts simple and then gets complicated and speed of response to an input does not make for a good control system see also computer control of aircraft.

I have given examples only but my knowledge or lack of it cost me an honours degree because of a Dr Sipson at what is now the Defence Academy because he refused to help me when I was suffering from cronic depression and didn't sit the final exam. He decided I should not be an Engineer and get a 2.1 degree as I understand it. Joke really considering I enjoyed the subject found it easy but had a real problem that I have now discovered went all the way back to Eulers Formulae even though I knew what it was in the real world and that error theory of control theory would have got me a first; if I could have remembered what e was that I knew at A level. Depression probably cost the world the combination of geometric space on a line with fermant symmetry in multi dimensional space and the primes and me getting $1M to tell you how to calculate them. Roll on UK Gov allowing me to study Maths on the dole eh? Human Right I think. JK Rowling wrote a book on the dole and I went to jail for it? See

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