On the approximate and analytical solutions to the fifth-order Duffing oscillator and its physical applications

Analytical approximations to a generalized forced damped complex Duffing oscillator: multiple scales method and KBM approach

“…There are many different and various equations of motion that were used for modeling several nonlinear oscillations in different physical and engineering systems [8][9][10][11]. Most published papers about the nonlinear oscillatory equations focused on the one-dimensional oscillatory differential equations that succeeded in explaining many different oscillations in different engineering, physical systems (especially in plasma physics), and statistical mechanics such as the Duffing oscillatory equation (DOE), the damped DOE [12], the forced damping DOE [13], the fifth-order DOE [14], the damped Helmholtz oscillator equation [15], the damped/ undamped Helmholtz-Duffing oscillatory equation [16], the Helmholtz-Fangzhu oscillator equation [17], the damped pendulum oscillator equation [18], and many others. On the other hand, there are some studies that have been conducted on the complex/coupled system of oscillatory differential equations [19][20][21][22].…”

Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators

“…[6][7][8][9][10] The simple pendulum has been used as a physical model to several solve problems related to many realistic and physical problems, for example, nonlinear plasma oscillations, [11][12][13] Duffing oscillators, [14][15][16][17] Helmholtz oscillations, 18 the nonlinear equation of wave, 19 and many other oscillators. [20][21][22][23][24][25] It is know that the main objective of the numerical approaches is to find some numerical solutions to various realistic physical, engineering, and natural problems, especially when exact solutions are unavailable or extremely difficult to determine. There are many numerical approaches that were used for analyzing the family of the Duffing oscillator and Duffing-Helmholtz oscillator with constant coefficients.…”

Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method

“…e pendulum oscillator and some related equation have been used as a physical model to solve several natural problems related to bifurcations, oscillations, and chaos such as nonlinear plasma oscillations [1][2][3][4][5][6][7][8][9], Du ng oscillators [10][11][12][13][14], and Helmholtz oscillations [12], and many other applications can be found in [15][16][17][18][19][20][21][22][23][24]. ere are few attempts for analyzing the equation of motion of the nonlinear damped pendulum taking the friction forces into account [25].…”