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*) = *te*^{4t}, *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:

**SOLUTION:**

*f(t)* = 2*U(t)* − 4*U*(*t* − 1) + 2*U*(*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

we obtain,

**I2.5.** Determine the final value of *c(t)* when the Laplace ...

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