My suggestions:

Write less, not more.

Read up on some math:
1. displacement, velocity, and acceleration are vectors
2. derivatives of harmonic functions involve phase shifts, this is not a choice, it is how trig functions work (remember how derivative of sin(x) is cos(x)?).
3. check out "aliasing" and "the Nyquist" when differencing to estimate a derivative.

Use the appropriate units (stress) when possible, because quantities like displacement and velocity
do not cause earthquakes.

John