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Quiz

# quiz 5 (10).pdf

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Queen's University

Mathematics & Engineering Courses

MTHE 225

Gregory G Smith

Fall

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Quiz 5a Solutions
1
1. (5 marks) Find the inverse Laplace transform of F(s) =
s + 2s + s
We wish to ﬁnd A,B,C such that
1 A B C
F(s) = 3 2 = + + 2
s + 2s + s s (s + 1) (s + 1)
Multiplying both sides by s(s + 1) , this equation becomes
2
1 = A(s + 1) + Bs(s + 1) + Cs (1)
Plugging in s = 0 gives A = 1. Plugging in s = −1 gives C = −1. To ﬁnd B,
diﬀerentiate both sides of equation (1) and plug in s = −1 to ﬁnd B = −1. Thus
1 1 1
F(s) = s − s + 1− (s + 1)
= L {1} − L {e } − L {te }−t
so
−t −t
f(t) = 1 − e − te

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