12 d*x(t) 5 dt3 d²x(t) dt² + 5x(t) = 3cos(2t) d²x(0) 2, dt2 dx(0) 1, dt x(0) = 1 3s2 + 5s + 1 X(s) : (s² + 15s + 34) 2 y(t) = 5e-5t

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find the Laplace transform and the inverse Laplace transform of the functions.

d²x(t)
- 8-
5 dt3
12 d³x(t)
+ 5x(t) = 3cos(2t)
dt2
d?x(0)
= 2,
dx(0)
= 1,
dt
x(0) = 1
dt2
3s2 + 5s +1
X(s) =
(s² + 15s + 34)
2
y(t) = 5e-5
N I3
Transcribed Image Text:d²x(t) - 8- 5 dt3 12 d³x(t) + 5x(t) = 3cos(2t) dt2 d?x(0) = 2, dx(0) = 1, dt x(0) = 1 dt2 3s2 + 5s +1 X(s) = (s² + 15s + 34) 2 y(t) = 5e-5 N I3
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