Math 293,   Homework 5,   due Wed Oct 2  in lecture.

Remember, we are expecting you to do whatever you need to do to be
confident about the problems we assign  whether or not we ask you
to hand them in.

 *) 3.1.1-16  (verify  proposed solutions, find c1 and c2 to satisfy ICs)
    Hand in none.

 *) 3.1.17-19 (show that nonlinear equations do not satisfy superposition.
    Hand in none.

 *) 3.1.20-26 (check to see if one function is a constant times the other).
    Hand in none.

 *) 3.1.27 (show how to use sum of homogeneous (complementary and particular solutions),
    3.1.27 (special case of the above).
    Hand in neither.

 *) 3.1.33-42 (solve constant coefficient equations).
    You should be able to solve all of these UNLESS you get repeated roots
    (in which case you can learn about how to solve from the book if you
    are interested).
    Hand in none.

 *) 3.3.1-9 and 21-23 (solving const coefficient equations).
    You should be able to do all of these UNLESS you get repeated roots.
    Hand in none.

 *) 3.4  we are not covering this section on mechanical vibrations, per se.
    But none of the math is hard and, with some thought you should be
    able to do most of the problems in this chapter if you are interested.

 *) 3.5.1-10, 31-35,(you should be able to do most of these problems, ok if you
    get stuck on a few).

 *) 3.6.1-14 (you should be able to do most of these).


*) You should know these six cases cold (with C>0)
   a) Solve  x'' + Cx = 0           with x(0)=x0, x'(0)=0.
   b) Solve  x'' + Cx = 0           with x(0)=0,  x'(0)=v0.
   c) Solve  x'' + Cx = 0           with x(0)=x0, x'(0)=v0.
   d) Solve  x'' - Cx = 0           with x(0)=x0, x'(0)=0.
   e) Solve  x'' - Cx = 0           with x(0)=0,  x'(0)=v0.
   f) Solve  x'' - Cx = 0           with x(0)=x0, x'(0)=v0.
The latter three are easier if you use sinh and cosh, though they are
not needed.

Hand in
^^^^^^^

1) a) Solve  mx'' + kx = sin(2 sqrt(k/m) t )   with x(0)=x0, x'(0)=0.

   b) Solve  mx'' + kx = sin(sqrt(k/m) t )     with x(0)=x0, x'(0)=0.
                    Why are the solutions so different?

2) Pick numbers a,b,c so that  ax'' + bx' + cx = 0 leads to real roots and find
    the general solution of the ODE.

3) Same as above but with complex roots and find the general REAL solution.