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

Figure 6

Amplitude-time response curves of (21) and (28) for the system parameter values of 𝑚=1/3, 𝐴=1, 𝜔_𝑛=2, ℎ=0.1, 𝑄=0.1, 𝜈=0.025, and 𝜔_𝑓=2 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) with 𝛼₂=4.3426, 𝛽=−1.3704, 𝛾=3.289, Δ=−3.508, 𝜀=1.3493, 𝛿=4.2695, 𝜖=−0.2956, 𝜈₁=0.2537, 𝜐=−10, and 𝜎=0.75.