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

Figure 3

Amplitude-time response curves, phase diagrams, and Morlet CWR plots of (17) and (18) for the system parameter values of 𝑎=1, 𝑏=−1, 𝜈=0.035, 𝑄=1, 𝜔_𝑓=2 with 𝑥(0)=57.3^∘ and 𝑥̇(0)=0. Here, the black solid line represents the numerical integration solution of (17), while the red dotted and red dashed lines represent the predictions obtained from the derived equivalent equation of motion (18). Here, 𝛼=1.999,𝛽=−0.1664, 𝛾=0.0079, 𝛿=1.999, 𝜖=−0.1613, and 𝜈₁=0.035.