In Problems 17 through 20, analyze the critical points of the indicated system, use a computer system to construct an illustrative position–velocity phase plane portrait, and describe the oscillations that occur.

The equations x' = y, y' = -sin x - 1/4 y |y| model a damped pendulum system as in Eqs. (34) and Fig. 9.4.10. But now the resistance is proportional to the square of the angular velocity of the pendulum. Compare the oscillations with those that occur when the resistance is proportional to the angular velocity itself.

Transcribed Image Text:

dx | dt dy dt = y, ―w² sin x - cy, (34)