A new exact solution of a damped quadratic non-linear oscillator |
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| Authors: | Jin-wen Zhu |
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| Institution: | State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030, China |
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| Abstract: | In this paper, we derive a new exact solution of the damped quadratic nonlinear oscillator (Helmholtz oscillator) based on the developed solution for the undamped case by the Jacobi elliptic functions. It is interesting to see that both of the damped Duffing oscillator and Helmholtz oscillator possess solutions that follow closely to the undamped case, and even the solution procedures are almost the same. |
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| Keywords: | Non-linear oscillator Jacobi elliptic function Exact solution |
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