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4. Consider the following piecewise-defined function f(t) on [0, ∞0): 0, 0st<2 S(t) = { 2t – 4, 2

4. Consider the following piecewise-defined function f(t) on [0, ∞0): 0, 0st<2 S(t) = { 2t – 4, 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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-3s2 + 2s +4l ( 62 – 4s + 5)(s – 2) S' 1. Calculate the inverse Laplace transform L-1 2. Solve the initial value problem by the method of Laplace transforms: y" – 3y – 4y = 12eª, y(0) = 2, y'(0) = -1 3. Solve the initial value problem by the method of Laplace transforms: y" + 4y = 2, y(0) = 4, y'(0) = 1 4. Consider the following piecewise-defined function f(t) on [0, 0): 0, 0<t<2 f(t) = { 2t – 4, 2<t<3 10e-, t>3 (a) Sketch the graph of f(t). (b) Rewrite f(t) as a linear combination of multiples of shifted Heaviside functions u(t – a), where the coefficients are functions of t. (c) Calculate the Laplace transform of f(t).
Transcribed Image Text:-3s2 + 2s +4l ( 62 – 4s + 5)(s – 2) S' 1. Calculate the inverse Laplace transform L-1 2. Solve the initial value problem by the method of Laplace transforms: y" – 3y – 4y = 12eª, y(0) = 2, y'(0) = -1 3. Solve the initial value problem by the method of Laplace transforms: y" + 4y = 2, y(0) = 4, y'(0) = 1 4. Consider the following piecewise-defined function f(t) on [0, 0): 0, 0<t<2 f(t) = { 2t – 4, 2<t<3 10e-, t>3 (a) Sketch the graph of f(t). (b) Rewrite f(t) as a linear combination of multiples of shifted Heaviside functions u(t – a), where the coefficients are functions of t. (c) Calculate the Laplace transform of f(t).
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