An AJP article describes a rubber-band oscillator whose stiffness
varies non linearly.
I've instead (since I have the apparatus) made one using permanent
magnets (Vernier low friction cart and track) The plot from the
output of a Vernier rotary motion sensor (PASCO linear accessory) is,
in the region of anharmonicity, "looks" a saw tooth. In the magnetic
far field the force evidently becomes linear, as the appearance
becomes sinusoidal. My problem: I want to fit the linear region to
a constant ** decay sinusoid to verify the oscillator's harmonicity.
I think I'm math challenged here; what's the equation?
And for the saw tooth I need to fit with a Fourier series; again a
constant decay. Again what is it. I can look this up and try with
various coefficients, etc., but I'm pressed for time and I don't know
how to incorporate the signum function in an equation.
I easily convert the apparatus to a harmonic (coil springs)
oscillator. I think I'll have no trouble here fitting. The decay is
exponential.
** It appears a coulomb type friction is dominant, not a linear with
speed, i.e. exponential decay. This is curious, as I thought the
increased decay (over the spring oscillator) was due to eddy
currents. It may be due to lack of rigidity.
bc not "really" lazy and thinks he's cleaned up his writing.