Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. a" – 5æ' = 8(t – 5), ¤(0) = 8, x'(0) = 0. - Find the Laplace transform of the solution. X(s) = L {r(t)}= || help (formulas)
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. a" – 5æ' = 8(t – 5), ¤(0) = 8, x'(0) = 0. - Find the Laplace transform of the solution. X(s) = L {r(t)}= || help (formulas)
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.
æ" – 5æ' = 8(t - 5),
æ(0) = 8, x'(0) = 0.
|
Find the Laplace transform of the solution.
X(s) = L {x(t)} =
help
(formulas)
Obtain the solution x(t).
x(t) =
help
(formulas)
Express the solution as a piecewise-defined function and think about what
happens to the graph of the solution at t = 5.
if 0 <t < 5,
{
æ(t) :
if 5 <t < ∞.
help (formulas)
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