Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators

Figure 2

Amplitude-time response curves, phase diagrams, and Morlet CWT plots of (12) and (13), for the system parameter values of 𝜈=0.01, 𝐴=1, 𝐵=3.5, 𝐺=0.5, 𝑄₀=0.5, 𝜔_𝑓=0.5 with 𝑦(0)=1 and 𝑦(̇0)=0. Here, the black solid line represents the numerical integration solution of (12) while the red dotted and the red dashed lines represent the prediction obtained by using the derived equivalent equation of motion (13) with 𝛿=0.9838, 𝜖=3.7827, and 𝜈₁=0.0099.