Question

I’ve got a table of values telling me how the signal level changes over time and I want to simulate a harmonic oscillator driven by this signal. It does not matter if the simulation is not 100% accurate.
I know the frequency of the oscillator.
I found lots of formulas but they all use a sine wave as driver.

Answer 1

I guess you want to perform some time-discrete simulation. The well-known formulae require analytic input (see Green’s function). If you have a table of forces at some point in time, the typical analytical formulae won’t help you too much.

The idea is this: For each point in time t0, the oscillator has some given acceleration, velocity, etc. Now a force acts on it -according to the table you were given- which will change it’s acceleration (F = m * a). For the next time step t1, we assume the acceleration stays at that constant, so we can apply simple Newtonian equations (v = a * dt) with dt = (t1-t0) for this time frame. Iterate until the desired range in time is simulated.

The most important parameter of this simulation is dt, that is, how fine-grained the calculation is. For example, you might want to have 10 steps per second, but that completely depends on your input parameters. What we’re doing here, in essence, is an Eulerian integration of the equations.

This, of course, isn’t all there is – such simulations can be quite complicated, esp. in not-so-well behaved cases where extreme accelerations, etc. In those cases you need to perform numerical sanity checks within a frame, because something ‘extreme’ happens in a single frame. Also some numerical integration might become necessary, e.g. the Runge-Kutta algorithm. I guess that leads to far at this point, however.

EDIT: Just after I posted this, somebody posted a comment to the original question pointing to the “Verlet Algorithm“, which is basically an implementation of what I described above.