Euler's formula and damped harmonic motion resources

[Saoist]

hi guys,

doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do (half the class). we don't need to know it for the exam itself, but you know...curiosity. does anyone know of any good online resources about FHM and DHM, maths included, but which explains clearly and concisely?

one major problem i have is that I've never seen the result:

e^(ipt)=cos(pt)+isin(pt) before. saw this in the middle of the DHM derivation which we were shown for all of 30seconds, scribbled it down.does anyone have a good derivation for this please?

 

[DeadWolfe]

Actually it's the definition of the complex exponential.

But to see that it makes sense, simple plug ipt into the power series of e^x, and look at what you get.