ABSTRACT
Annotation. Free and forced oscillations of a torsion spring pendulum damped
by viscous and dry friction are investigated analytically and with the help of nu-
merical simulations. A simplified mathematical model is assumed (Coulomb law),
which nevertheless can explain many peculiarities in behavior of various oscilla-
tory systems with dry friction. The amplitude of free oscillations diminishes under
dry friction linearly, and the motion stops after a final number of cycles. The am-
plitude of a sinusoidally driven pendulum with dry friction grows at resonance
without limit if the threshold is exceeded. At strong enough non-resonant sinu-
soidal forcing, dry friction causes transients that typically lead to definite limit
cycles — periodic steady-state regimes of symmetric non-sticking forced oscilla-
tions that are independent of initial conditions. However, at the subharmonic sinu-
soidal forcing, interesting peculiarities of the steady-state response are revealed,
such as multiple coexisting regimes of asymmetric oscillations that depend on
initial conditions. Under certain conditions, simple dry friction pendulum shows
complicated stick-slip motions and chaos.
