Consider the following initial value problem, in which an input of largeamplitude and short duration has been idealized as a delta function.a" – 5x' = 8(t – 5),x(0) = 8,x'(0) = 0.Find the Laplace transform of the solution.X(s) = L {x(t)} =(e^(-5s)+8s-40)/(s^2-5)help(formulas)Obtain the solution x(t).I(t)(e^(-5s)+8s-40)/(s^2-5)help(formulas)Express the solution as a piecewise-defined function and think about whathappens to the graph of the solution at t = 5.8cossqrt(5t)+40/sqrt(5)sinscif 0

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Consider the following initial value problem, in which an input of large mplitude and short duration has been idealized as a delta function. a" – 5x' = 8(t – 5), x(0) = 8, x'(0) = 0. ind the Laplace transform of the solution. {(s) = L {x(t)} = (e^(-5s)+8s-40)/(s^2-5) help ormulas) obtain the solution x(t). (t) (e^(-5s)+8s-40)/(s^2-5) help ormulas) xpress the solution as a piecewise-defined function and think about what appens to the graph of the solution at t = 5. 8cossqrt(5t)+40/sqrt(5)sinsc if 0

Consider the following initial value problem, in which an input of large mplitude and short duration has been idealized as a delta function. a" – 5x' = 8(t – 5), x(0) = 8, x'(0) = 0. ind the Laplace transform of the solution. {(s) = L {x(t)} = (e^(-5s)+8s-40)/(s^2-5) help ormulas) obtain the solution x(t). (t) (e^(-5s)+8s-40)/(s^2-5) help ormulas) xpress the solution as a piecewise-defined function and think about what appens to the graph of the solution at t = 5. 8cossqrt(5t)+40/sqrt(5)sinsc 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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Question

Consider the following initial value problem, in which an input of large
amplitude and short duration has been idealized as a delta function.
a" – 5x' = 8(t – 5),
x(0) = 8,
x'(0) = 0.
Find the Laplace transform of the solution.
X(s) = L {x(t)} =
(e^(-5s)+8s-40)/(s^2-5)
help
(formulas)
Obtain the solution x(t).
I(t)
(e^(-5s)+8s-40)/(s^2-5)
help
(formulas)
Express the solution as a piecewise-defined function and think about what
happens to the graph of the solution at t = 5.
8cossqrt(5t)+40/sqrt(5)sinsc
if 0 <t< 5,
x(t)
if 5 <t < oo.
help (formulas)

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ISBN:

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Author:

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