Investigation of parametric resonance oscillations of mathematical pendulum variable length

Mathematics. Physics. Mechanics


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




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.


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

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