Abstract
A nonlinear oscillator with a damping term can model many nonlinear vibration problems. This short remark insights into its physical understanding by the variational principle, which is established by the semi-inverse method. The dissipative energy involved in the variational formulation can be explained by the two-scale thermodynamics. Taylor series method is used to solve its frequency-amplitude relation.
Highlights
We studied a nonlinear oscillator with a damping term; we found a typo in equation (1), which was wrongly written as[1] u€
We consider a spring vibrating in a fractal space,[14,15,16,17,18,19,20,21,22] for example, in water, when c 1⁄4 0, it is a linear spring, but it ignores the effects of water molecule’s size and distribution on its oscillatory property
When we study the vibration in the fractal space on a smaller scale, saying a molecular scale, the dissipative energy should be a function of the square of its velocity (u_ 2)
Summary
Keywords Semi-inverse method, variational principle, dissipative energy, Taylor series method, He’s frequency formulation We studied a nonlinear oscillator with a damping term; we found a typo in equation (1), which was wrongly written as[1] u€
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