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Debunking the Linear Damping Model for Mechanical Harmonic Oscillators |
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Earlier experiments as a
function of frequency suggested that internal friction damping of mechanical
oscillators may be significantly nonlinear.
As such, experiment would be in violation of the widespread belief
that damping friction is proportional to velocity (commonly called viscous
damping). In a recent set of
experiments, a folded pendulum was driven to steady state at drive frequencies
below resonance. Motion at the natural
frequency was observed not to decay toward zero in transient manner, as
required by the common theory. It was instead observed to persist at
levels significantly above noise, when the frequency of the sub-resonance
drive was 1/n, where n = odd integer.
Although this behavior cannot be explained by linear damping models, the
figure below shows that it can be explained by the nonlinear modified Coulomb
model developed by the author. Also
observed was a surprisingly large distortion in the steady state response, for
drive frequency = 1/2. Shown to be
independent of drive intensity, this distortion can be explained by
anisotropy ― different friction forces for opposite directions of the
motion. Moreover, for agreement
between the nonlinear theory and experiment, the damping must be negative
during one set of half-cycles of the motion. |
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for light refreshments at 4:15pm outside WSC 109.