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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-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)*

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)*

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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