Question

3. Find the time function corresponding to each of the following Laplace transforms using partial-function expansions: a. $F(s) = \frac{2}{s(s+2)}$ b. $F(s) = \frac{10}{s(s+1)(s+10)}$ c. $F(s) = \frac{3s+2}{s^2+4s+20}$ d. $F(s) = \frac{1}{s^2+4}$ e. $F(s) = \frac{2(s+2)}{(s+1)(s^2+4)}$

          3.
Find the time function corresponding to each of the following Laplace transforms using
partial-function expansions:
a.
\(F(s) = \frac{2}{s(s+2)}\)
b.
\(F(s) = \frac{10}{s(s+1)(s+10)}\)
c.
\(F(s) = \frac{3s+2}{s^2+4s+20}\)
d.
\(F(s) = \frac{1}{s^2+4}\)
e.
\(F(s) = \frac{2(s+2)}{(s+1)(s^2+4)}\)

3.
Find the time function corresponding to each of the following Laplace transforms using
partial-function expansions:
a.
F(s) = (2)/(s(s+2))
b.
F(s) = (10)/(s(s+1)(s+10))
c.
F(s) = (3s+2)/(s^2+4s+20)
d.
F(s) = (1)/(s^2+4)
e.
F(s) = (2(s+2))/((s+1)(s^2+4))

Added by Geoffrey B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

10/06/2022

Step 1

$$F(s) = \frac{2}{s(s+2)}$$ We can use partial fraction decomposition to rewrite this expression as: $$\frac{2}{s(s+2)} = \frac{A}{s} + \frac{B}{s+2}$$ Multiplying both sides by $s(s+2)$ gives: $$2 = A(s+2) + Bs$$ Setting $s=0$ gives $A=1$. Setting $s=-2$ gives Show more…

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3. Find the time function corresponding to each of the following Laplace transforms using partial-function expansions: a. $$F(s) = \frac{2}{s(s+2)}$$ b. $$F(s) = \frac{10}{s(s+1)(s+10)}$$ c. $$F(s) = \frac{3s+2}{s^2+4s+20}$$ d. $$F(s) = \frac{1}{s^2+4}$$ e. $$F(s) = \frac{2(s+2)}{(s+1)(s^2+4)}$$