I am asking this for a damped oscillator in this situation: oscillator What if there are two damping forces present, one being friction and the other being air resistance? When the damping force is dependent on velocity, I have read that the decay of the oscillator's amplitude can be given as an exponential function. If the damping force is constant in the case of friction, then this decay could be modeled by a straight line (I think?). If both damping forces are present, could the decay be modeled by a different type of function, or just the sum of both functions?

I am asking this because of a practical I am doing at school. I set up my apparatus as it is above but with two springs either side, and a large square card on top to increase air resistance. I recorded the amplitude for each oscillation until the oscillator had stopped with time. When I plotted an lnA/t graph, I found that the the amplitude was probably decaying exponentially at lower times (because the data followed a roughly straight line), but this relationship broke down at smaller oscillations. This made sense if I considered the damping being composed to two components with one being constant and the other dependent on velocity, because at low velocities (smaller oscillations) the component dependent on velocity would be very small. I did try to see if the data fit other relationships, for example when I plotted a sqrt(A)/t graph, the data seemed to fit a straight line. Is this a coincidence, or is there a more general function that can describe the decay of the oscillator's amplitude?

  • $\begingroup$ I'd expect a sudden stop, since for smaller amplitudes the friction force should exceed the force from the spring and arrest the block immediately. $\endgroup$ – stafusa Dec 21 '17 at 8:13

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