8. Suppose we take / = 9.8 m (so g/I = 1), m 1, and b large, say b = 4. For the damped pendulum system above and with this choice of parameter values, do the following. (a) Find the cigenvalues and...

Solve all the subparts else leave , you own answers, at chegg given the worng answer not copy any solution , do not type

Extracted text: 8. Suppose we take / = 9.8 m (so g/I = 1), m 1, and b large, say b = 4. For the damped pendulum system above and with this choice of parameter values, do the following. (a) Find the cigenvalues and eigenvectors of the linearized system at the equilib- rium point (0, 0). (b) Find the eigenvalues and eigenvectors of the linearized system at the equilib- rium point (7, 0). (c) Sketch the phase portrait near the equilibrium points. (d) Sketch the entire phase portrait. [Hint: Begin by sketching the level sets of H as in the text.]


Extracted text: In Exercises 4-11, we consider the damped pendulum system de dt ap dt b sine -v, m where b is the damping coefficient, m is the mass of the bob, I is the length of the arm, and g is the acceleration of gravity (g 9.8 m/s?).