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g) x" +0.4x + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0.

g) x" +0.4x + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 43E
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aula and plot f(t) on [0, ∞). lot the function 6, bet-3, 0, and find the Laplace tranform X (s). 0≤t<3, 3<t<4, -4, 4≤t<6, t≥6, DY 6. Solve the following initial value problems using Laplace transform a) x² + 5x = H (t-2), x(0) = 1. b) x² + x = sin 2t, x(0) = 0. c) z" - r' - 6x=0, d) z" - 2x' + 2x=0, e) r" - 2x² + 2x = e-t, f) r" -r' =0, x(0) = 1, x'(0) = 0. g) x" +0.4x + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0. h) 2" + 9x = sin 3t, x(0) = 0, '(0) = 0. i) r"-2x = 1, r(0) = 1, r'(0) = 0. j) r' = 2x + H(t-1), x(0) = 0. 7. Sketch the function f(t) transform. x(0) = 2, r'(0) = -1 x(0)=0, x'(0) = 1. = r(0) = 0, x'(0) = 1. 4) as a multi 8. Find the Laplace transform of f(t) = t²H(t - 3). 9. Invont 2H(t-3) - 2H(t - 4) and fin
Transcribed Image Text:aula and plot f(t) on [0, ∞). lot the function 6, bet-3, 0, and find the Laplace tranform X (s). 0≤t<3, 3<t<4, -4, 4≤t<6, t≥6, DY 6. Solve the following initial value problems using Laplace transform a) x² + 5x = H (t-2), x(0) = 1. b) x² + x = sin 2t, x(0) = 0. c) z" - r' - 6x=0, d) z" - 2x' + 2x=0, e) r" - 2x² + 2x = e-t, f) r" -r' =0, x(0) = 1, x'(0) = 0. g) x" +0.4x + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0. h) 2" + 9x = sin 3t, x(0) = 0, '(0) = 0. i) r"-2x = 1, r(0) = 1, r'(0) = 0. j) r' = 2x + H(t-1), x(0) = 0. 7. Sketch the function f(t) transform. x(0) = 2, r'(0) = -1 x(0)=0, x'(0) = 1. = r(0) = 0, x'(0) = 1. 4) as a multi 8. Find the Laplace transform of f(t) = t²H(t - 3). 9. Invont 2H(t-3) - 2H(t - 4) and fin
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