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
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
icon
Related questions
Question
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)*
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning