Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. a" + 1672x = 4T8(t – 2), æ(0) = 0, x'(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help (formulas) Obtain the solution x(t). x(t) = sin(4pit-8pi)(4(t-2)) help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. sin(4pi(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. a" + 1672x = 4T8(t – 2), æ(0) = 0, x'(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help (formulas) Obtain the solution x(t). x(t) = sin(4pit-8pi)(4(t-2)) help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. sin(4pi(t-2)) 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.
x" + 167°x =
. Από (t-2 )
x(0) = 0, a'(0) = 0.
Find the Laplace transform of the solution.
X(s) = L {x(t)}
%3D
help
(formulas)
Obtain the solution x(t).
x(t)
sin(4pit-8pi)(4(t-2))
help
(formulas)
Express the solution as a piecewise-defined function and think about what
happens to the graph of the solution at t =
= 2.
sin(4pi(t-2))
if 0 <t< 2,
x(t) =
if 2 <t < ∞.
help (formulas)
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