Okay simple harmonic motion:
Theres two different formulas you can have, depending on wether the motion starts at the top (release a pendulum) or at the bottom (hit a pendulum). These are:
X=aCos ((2piF)t) and X=aSin((2piF)t)
Differentiate to get:
V=-(2piF)*aSin((2piF)t) and V=(2piF)*aCos((2piF)t)
Whichever one of these you use, you can rearrange to get:
V^2 = (2piF)^2*(a^2-X^2)
If you differentiate the velocity one again, you get:
Acc = -(2piF)^2*aCos((2piF)t) and Acc = -(2piF)^2*aSin((2piF)t)
BUT you hardly ever use these, as the second chunk of each is equal to the X from the top of each column, so in both cases:
Acc = -(2piF)^2 * X <--- and this is the key SHM equation, as if any situation can be written as this, then all the above equations are true.
NB - I personally would rewrite 2piF as omega, (the squiggly w) to save writing it out every time.
Hope that helps, luke (and hope i got them all right)