Investigation of parametric resonance oscillations of mathematical pendulum variable length

Mathematics. Physics. Mechanics


Аuthors

Krasilnikov P. S.*, Storozhkina T. A.

,

*e-mail: kaf803@mai.ru

Abstract

When the length of mathematical pendulum varies according harmonious law with small amplitude, linear and nonlinear oscillations of pendulum at resonance 1:2 are researched. It is shown that the non-linear change of time reduce the equation of linear oscillations to Mathieu’s equation. The approximate analytical solution of Mathieu’s equation at resonance 1:2 is obtained. The non-linear equation containing terms of third order is considered. Amplitude- frequency characteristic of resonance oscillations was obtained, it is shown also that amplitude of oscillations takes finite value as opposed to unlimited values of linear approaching.

Keywords:

parametric oscillations, resonance, stability of equilibrium, Mathieu’s equalization.


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