Geodesic
OSCILLATOR WITH STRONG QUADRATIC DAMPING FORCE
Publications de l'Institut Mathématique, _N_S_85 (2009) no. 99, p. 119 .

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Oscillations of a system with strong quadratic damping are considered. For the exact analytical form of the energy-displacement function the explicit form of the maximal amplitudes of vibration are obtained by introducing the Lambert-w function. Comparing the neighbor maximal amplitudes and the corresponding energies the conclusions about the energy dissipation is given. The approximate solution for a strong nonlinear differential equation which describes the motion of the oscillator with quadratic damping is calculated applying the elliptic-harmonic-balance method. The accuracy of the solution is affirmed by comparing the maximal displacements obtained using the approximate method with the exact one obtained by energy method.
DOI : 10.2298/PIM0999119C
Classification : 34C15 
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     author = {Livija Cveti\'canin},
     title = {OSCILLATOR {WITH} {STRONG} {QUADRATIC} {DAMPING} {FORCE}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {119 },
     publisher = {mathdoc},
     volume = {_N_S_85},
     number = {99},
     year = {2009},
     doi = {10.2298/PIM0999119C},
     zbl = {1224.34107},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0999119C/}
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Livija Cvetićanin. OSCILLATOR WITH STRONG QUADRATIC DAMPING FORCE. Publications de l'Institut Mathématique, _N_S_85 (2009) no. 99, p. 119 . doi : 10.2298/PIM0999119C. http://geodesic.mathdoc.fr/articles/10.2298/PIM0999119C/

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