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Consider the initial value problem for function y given by, where u(t - c) denotes the step function with step at t = c. ▸ Part 1: Finding F(s) ▸ Part 2: Finding Y(s) ▾ Part 3: Rewriting Y(s) (c) The function Y(s) found in part (a) has a partial fraction decomposition Y(s) = e-38 y" - 2 y - 15y = 5 u(t-3) e¹t, A (sa) where we assume that a > b> c. Find the constants A, B, C, a, b, and c. Σ B = Σ A = Σ Recall: In your answer a > b > c. Part 4: Finding y(t) a = 5 b = 4 Σ + y(0) = 0, B (s - b) C = + -3 y' (0) = 0. Σ Σ

Consider the initial value problem for function y given by, where u(t - c) denotes the step function with step at t = c. ▸ Part 1: Finding F(s) ▸ Part 2: Finding Y(s) ▾ Part 3: Rewriting Y(s) (c) The function Y(s) found in part (a) has a partial fraction decomposition Y(s) = e-38 y" - 2 y - 15y = 5 u(t-3) e¹t, A (sa) where we assume that a > b> c. Find the constants A, B, C, a, b, and c. Σ B = Σ A = Σ Recall: In your answer a > b > c. Part 4: Finding y(t) a = 5 b = 4 Σ + y(0) = 0, B (s - b) C = + -3 y' (0) = 0. Σ Σ

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section5.3: Partial Fractions
Problem 7E
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Consider the initial value problem for function y given by, where u(t - c) denotes the step function with step at t = c. ▸ Part 1: Finding F(s) ▸ Part 2: Finding Y(s) ▾ Part 3: Rewriting Y(s) (c) The function Y(s) found in part (a) has a partial fraction decomposition A + (s - a) where we assume that a > b > c. Find the constants A, B, C, a, b, and c. Σ B = Σ A = a = 5 y" - 2 y - 15y = 5 u(t-3) e¹t, Σ Recall: In your answer a > b> c. Part 4: Finding y(t) b= 4 Y(s) = e-3s Σ y(0) = 0, B (s - b) C = + -3 y' (0) = 0. Σ Σ
Transcribed Image Text:Consider the initial value problem for function y given by, where u(t - c) denotes the step function with step at t = c. ▸ Part 1: Finding F(s) ▸ Part 2: Finding Y(s) ▾ Part 3: Rewriting Y(s) (c) The function Y(s) found in part (a) has a partial fraction decomposition A + (s - a) where we assume that a > b > c. Find the constants A, B, C, a, b, and c. Σ B = Σ A = a = 5 y" - 2 y - 15y = 5 u(t-3) e¹t, Σ Recall: In your answer a > b> c. Part 4: Finding y(t) b= 4 Y(s) = e-3s Σ y(0) = 0, B (s - b) C = + -3 y' (0) = 0. Σ Σ
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