#### BELIEVE   ME   NOT!    - -     A   SKEPTIC's   GUIDE   Next: The Spring Pendulum Up: Simple Harmonic Motion Previous: Projecting the Wheel

# Simple Harmonic Motion

The above mechanical example serves to introduce the idea of and as functions in the sense to which we have (I hope) now become accustomed. In particular, if we realize that (by definition) and ,  the formulae for  vx(t)  and  ax(t) represent the derivatives of  x(t):
 x = (13.4) = (13.5) = (13.6)

-- which in turn tell us the derivatives of the sine and cosine functions: = (13.7) = (13.8)

So if we want we can calculate the derivative of a sine or cosine function almost as easily as we did for our "old" friend the exponential function. I will not go through the details this time, but this feature again allows us to express these functions as series expansions: (13.9)

where I have shown the exponential function along with the sine and cosine for reasons that will soon be apparent.   Next: The Spring Pendulum Up: Simple Harmonic Motion Previous: Projecting the Wheel
Jess H. Brewer - Last modified: Sun Nov 15 13:35:44 PST 2015