5.4-18
The characteristic equation for the damped system is 2(r^2+6r+25)=0 with
roots r=-3+4i,r=-3-4i. Atoms=e^{-3t}cos 4t, e^{-3t}sin 4t. Underdamped.

The characteristic equation for the undamped system is 2(r^2+0+25)=0 with
roots r=5i,r=-5i. Atoms=cos 5t, sin 5t.

Solve each homogeneous system. Evaluate constants using the initial
conditions x(0)=0, x'(0)=-8. This is a linear algebra problem.

Write each solution in phase-amplitude form, a trig problem.


5.4-34
Use the results freely from problems 32 and 33 to solve problem 34.
Let x1=6.73 and x2=1.46 in problem 33. Use times t1=0.34 and t2=1.17
in problem 32.

The phase-amplitude form of the solution, as described on pp 323-324, is
used to solve the problem. Ideas from these pages are used to solve
problems 32 and 33.

See also (21) to (23) page 327, for relations between m,c,k and the 
symbol omega used in problems 32 and 33.