Torsion Spring Oscillator with Dry Friction

Free and forced oscillations of a torsion spring pendulum damped by viscous and dry (Coulomb) friction are investigated analytically and with the help of computer simulations. An idealized mathematical model of dry friction described by the so-called z-characteristic is assumed. This simple physical model can explain many peculiarities in behavior of various oscillatory systems with dry friction. The amplitude of free oscillations diminishes under dry friction linearly, and the motion stops after a final number of cycles. In the sinusoidally driven pendulum with dry friction, the amplitude of forced oscillations grows linearly without limit at resonance if the threshold is exceeded. At strong enough non-resonant sinusoidal forcing dry friction causes transients that typically lead to periodic steady-state regimes of symmetric non-sticking forced oscillations which are independent of initial conditions. However, at the subharmonic sinusoidal forcing interesting peculiarities of the steady-state response are revealed such as multiple regimes of asymmetric oscillations that depend on initial conditions. Under certain conditions simple dry friction pendulum shows complicated stick-slip motions and chaos.