Let P(s) and Q(s) be polynomials with the degree of P(s) less than the degree of Q(s). Let Q(s) = (s-r₁) (s-r₂2). (srn), where the rk's are distinct real numbers. Given these conditions, Heaviside's expansion formula states that n € ¹{B}(M)= (t) = Σ -erkt. Use Heaviside's expansion formula to determine the P (rk) Q' (Tk) k=1 inverse Laplace transform of F(s) = 3s²-14s+7 (S-2)(s-4)(s+5)*

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 43E
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Let P(s) and Q(s) be polynomials with the degree of P(s) less than the degree of Q(s). Let
Q(s) = (s-r₁) (s-r₂) (srn), where the rk's are distinct real numbers. Given
these conditions, Heaviside's expansion formula states that
P (rk)
n
P
€¯- ¹ {8} (0) = £
L
k=1
...
-erkt. Use Heaviside's expansion formula to determine the
Q'
Q (™K)
inverse Laplace transform of F(s) =
3s² - 14s+7
(s-2)(s-4) (s+5)*
Transcribed Image Text:Let P(s) and Q(s) be polynomials with the degree of P(s) less than the degree of Q(s). Let Q(s) = (s-r₁) (s-r₂) (srn), where the rk's are distinct real numbers. Given these conditions, Heaviside's expansion formula states that P (rk) n P €¯- ¹ {8} (0) = £ L k=1 ... -erkt. Use Heaviside's expansion formula to determine the Q' Q (™K) inverse Laplace transform of F(s) = 3s² - 14s+7 (s-2)(s-4) (s+5)*
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