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y" + 9n²y = 3ñd(t – 4), a. Find the Laplace transform of the solution. Y(s) = L{y(t)} b. Obtain the solution y(t). y(t): y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. = { y(0) = 0, y'(0) = 0. if 0 ≤ t < 4, if 4 < t < c.

y" + 9n²y = 3ñd(t – 4), a. Find the Laplace transform of the solution. Y(s) = L{y(t)} b. Obtain the solution y(t). y(t): y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. = { y(0) = 0, y'(0) = 0. if 0 ≤ t < 4, if 4 < t < c.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 9n² y 3πd(t – 4), a. Find the Laplace transform of the solution. = Y(s) = L{y(t)} b. Obtain the solution y(t). y(t) y(t) = = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. - { y(0) = 0, y'(0) = 0. if 0 ≤ t < 4, if 4 < t < ∞. ).
Transcribed Image Text:Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 9n² y 3πd(t – 4), a. Find the Laplace transform of the solution. = Y(s) = L{y(t)} b. Obtain the solution y(t). y(t) y(t) = = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. - { y(0) = 0, y'(0) = 0. if 0 ≤ t < 4, if 4 < t < ∞. ).
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