Consider a damped driven Pendulum, of mass m and length L, with damping and a driving force of magnitude F at frequency w. You can consider either the vertically driven pendulum, where the driving force is F sin cos wt or a tangentially driven pendulum with dring force F cos wt. (a) In the limit of zero dampling and driving, what is the energy corresponding to motion on the separatrix between oscillations and rotations? (b) What damping results in approximately 1 /10 of the energy being lost in one oscillation (c) What driving force F results in a gain of approximately 1/10 of the energy in part (a) (d) Do you expect the driving and damping in your answers to (b) and (c) to result in or rotation? in one oscillation or rotation? chaotic motion? Why or why not? Computationally explore the dynamics for those paramctcrs, and show whcther or not chaotic motion occurs. (e) How does the motion depend on the driving frequency w? Consider a damped driven Pendulum, of mass m and length L, with damping and a driving force of magnitude F at frequency w. You can consider either the vertically driven pendulum, where the driving force is F sin cos wt or a tangentially driven pendulum with dring force F cos wt. (a) In the limit of zero dampling and driving, what is the energy corresponding to motion on the separatrix between oscillations and rotations? (b) What damping results in approximately 1 /10 of the energy being lost in one oscillation (c) What driving force F results in a gain of approximately 1/10 of the energy in part (a) (d) Do you expect the driving and damping in your answers to (b) and (c) to result in or rotation? in one oscillation or rotation? chaotic motion? Why or why not? Computationally explore the dynamics for those paramctcrs, and show whcther or not chaotic motion occurs. (e) How does the motion depend on the driving frequency w