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

Figure 5

Amplitude-time response curves of (21) and (28) for the system parameter values of 𝑚=8/5, 𝐴=1, 𝜔_𝑛=0, ℎ=10, 𝑄=10, 𝜈=0.1, and 𝜔_𝑓=3 with 𝑥(0)=1 and 𝑥̇(0)=0. Here, the red solid and black dashed lines represent, respectively, the numerical integration solution of (21) and (28), while the purple triangles represent the approximate solution of (21) derived in [5] with 𝛼₂=3.0954, 𝛽=21.2256, 𝛾=−36.7078, Δ=35.2187, 𝜀=−12.8501, 𝛿=3.5311, 𝜖=3.6588, 𝜈₁=0.1155, 𝜐=−50, and 𝜎=−1.22.