Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 4π²y = 2πd(t − 2), y(0) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = b. Obtain the solution 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 = 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" + 4π²y = 2πd(t − 2), y(0) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = b. Obtain the solution 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 = if 0
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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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" + 4π²y:
=
2πd(t − 2),
y(0) = 0, y(0) = 0.
a. Find the Laplace transform of the solution.
Y(s) = L{y(t)} =
=
b. Obtain the solution 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 = 2.
if 0 ≤t < 2,
y(t)
}-
if 2<t< ∞.
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