Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 5x' = 8(t - 4), a(0) = 6, a'(0)= 0. In the following parts, use h(t - c) for the Heaviside function h (t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution a(t). c(t)

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 5x' = 8(t - 4), a(0) = 6, a'(0)= 0. In the following parts, use h(t - c) for the Heaviside function h (t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution a(t). c(t)

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:
x" – 5x' = 8(t – 4),
x(0) = 6, x'(0)= 0.
-
In the following parts, use h(t – c) for the Heaviside function h(t) if necessary.
a. Find the Laplace transform of the solution.
L{x(t)}(s) =
b. Obtain the solution x(t).
x(t)

c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at
t = 4.
if 0 <t < 4,
a (t) =
if 4 <t < ∞.

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