C++ program, Chaotic Behavior(nonlinear driven pendulum,Lypanov Exponents)

Simple C++ program that simulates behavior of a nonlinear damped driven pendulum. Second program that using Lyanpunov exponents. It should take long or be too long or complicated. As simple as possible please. We just learned about Classes and Structures in class so that is the level im looking for. This is a copy paste of the pdf. If anything is unclear please let me know and ill attach the origional. 1. (⋆)Exploring Poincar´e Sections. Simulate the nonlinear driven pendulum, given by where ωd Fd are the frequency and amplitude of the driving force, and q is a parameter that controls the damping. Produce a Poincar´e section of this system (ω as a fuction of θ) where the sampling is in phase with the driving force. As a starting point, use q = 0.5 ; ω = 1.0 ; Fd = 1.2 ; ωd = 2/3. How sensitive is the section to variations in the parameters? Try adjusting the phase of the sampling to ±π/4 to see how (and if ) the Poincar´e section changes. And finally, do a high??"resolution study of the Poincar´e section for θ > 2. See if you can find more structure in the attractor than was apparent in your original plot. 2. Lyapunov Exponents. In the case where the damped and driven nonlinear pendulum has q = 1/2, ωo = 1, and ωd = 2/3, find the driving amplitude (F ) at which the system crosses over into chaos. Do this by calculating Lyapunov exponents for a variety of F ’s, and noting where λ = 0. ## Deliverables 1) All deliverables will be considered "work made for hire" under U.S. Copyright law. Employer will receive exclusive and complete copyrights to all work purchased. (No 3rd party components unless all copyright ramifications are explained AND AGREED TO by the employer on the site per the worker's Worker Legal Agreement). ## Platform Using C++ , Unix. I have cygwin on my PC at home.