2.30 ILLUSTRATIVE PROBLEMS AND SOLUTIONS
This section provides a set of illustrative problems and their solutions to supplement the material presented in Chapter 2.
I2.1. Determine the poles and zeros of
SOLUTION: Simple poles are located at s = 0, −2, −6
Pole of order two located at −8
Simple zeros located at −1, −4
I2.2. Determine the Laplace transform of f(t) which is given by
f(t) = te4t, t ≥0
f(t) = 0, t > 0.
SOLUTION: From Appendix A, eighth item: For n = 2 and a = −4, we obtain
I2.3. Determine the Laplace transform F(s) for the function f(t) illustrated:
f(t) = 2U(t) − 4U(t − 1) + 2U(t − 2)
From Table 2.1, item 2, and the time-shifting theorem, we obtain
I2.4. Determine the initial value of c(t) where the Laplace transform of C(s) is given by:
SOLUTION: From the initial-value theorem
I2.5. Determine the final value of c(t) when the Laplace ...