Damped harmonic motion sinusoid equation

[biles1234]

what is the equation? i have something written down in my notes but i really don't get it...

x=A(e^-kt)(cos omega t)

first of all, how is the amplitude calculated if it decreases over time?? is it averaged?

what is e?

second of all, to calculate k, you need hooke's law and you need displacement. is this displacement averaged over time as well?

what is omega??

and what cos of what angle is used??

sorry if I'm being really vague but I'm really confused about this. thank you.

 

[Tide]

1) The "amplitude" A is the initial amplitude.

2) e Euler's number - the base of natural logarithms = 2.718281728...

3) x IS the displacement.

4) omega is the circular frequency of the oscillation (in this case corrected for damping)

5) "cos" is the cosine (a trigonometric function) and you treat $\omega t$ as the angle (i.e. the phase of the oscillation).