Chapter 2, Problem 2.32P

For each of the following equations, determine the transfer function X(s)/F(s) and compute the characteristic roots:

1. $5\stackrel{\dot{}}{x}+7x=15f\left(t\right)$
2. $3\ddot{x}+30\stackrel{\dot{}}{x}+63x=5f\left(t\right)$
3. $\ddot{x}+10\stackrel{\dot{}}{x}+21x=4f\left(t\right)$
4. $\ddot{x}+14\stackrel{\dot{}}{x}+49x=7f\left(t\right)$
5. $\ddot{x}+14\stackrel{\dot{}}{x}+58x=6f\left(t\right)+4f\left(t\right)$
6. $5\stackrel{\dot{}}{x}+7x=4f\left(t\right)+15f\left(t\right)$