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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" – 8y = 6(t – 2), y(0) = 1, y(0) = 0. a. Find the Laplace transform of the solution. Y (s) = L {y(t)} b. Obtain the solution y(t). Use h(t – a) for the Heaviside function shifted a units horizontally. (Class notes have ua(t) = h(t – a).) y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" – 8y = 6(t – 2), y(0) = 1, y(0) = 0. a. Find the Laplace transform of the solution. Y (s) = L {y(t)} b. Obtain the solution y(t). Use h(t – a) for the Heaviside function shifted a units horizontally. (Class notes have ua(t) = h(t – a).) y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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" – 8y' = 8(t – 2), y(0) = 1, y(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} b. Obtain the solution y(t). Use h(t – a) for the Heaviside function shifted a units horizontally. (Class notes have ua(t) = h(t – a).) y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0<t< 2, { y(t) : if 2 <t < o.
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" – 8y' = 8(t – 2), y(0) = 1, y(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} b. Obtain the solution y(t). Use h(t – a) for the Heaviside function shifted a units horizontally. (Class notes have ua(t) = h(t – a).) y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0<t< 2, { y(t) : if 2 <t < o.
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