HOW TO DESIGN NONLINEAR OSCILLATORS WITH AN AMPLITUDE-INDEPENDENT PERIOD

Ivana¹

¹ Kovacic

doi:10.20906/CPS/COB-2015-1575

Resumo

It is well-known that the dynamics of nonlinear oscillators in general involves a relationship between the amplitude of periodic motion and its period/frequency. There may be some situations where such dependence is undesirable. This raises the question of designing a system which is nonlinear, but whose period is constant and amplitude-independent, corresponding to the so-called isochronous motion. The solution to this problem is provided, both in terms of general mathematical and mechanical models by starting from a simple pendulum. The examples when the simple pendulum and its cubic approximation perform isochronous motion are also given. In addition, the issue of design of nonlinear systems that have a similar equation of motion but are damped is also addressed and illustrated.

Palavras-chave: nonlinear oscillators; isochronicity; pendulum; potential energy; kinetic energy