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Engineering Analysis Exam 1
Balance of forces for a damped linear oscillator gives
m
d
2
x
dt
2
=−
c
dx
dt
−
kx
h
t
where
c
,
k
,
m
are positive numbers.
(a) Write this differential equation in standard form.
(b) Classify this differential equation. Be as specific as possible.
(c) Find the general solution for the case
h(t) = 0
.
(d) If
h(t) = 0
,
x(0) = b
, and
x'(0) = 0
, find the particular solution
x(t)
.
(e) For this particular solution, distinguish three regimes in the behavior of
x(t)
at positive
t
, depending
on the relative values of
c
,
k
, and
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Unformatted text preview: m . (f) If h t = e − t , find a solution x(t) . Assume that e − t is not a homogenous solution. (g) Find the Laplace transform of the differential equation if h(t) = aδ(t) , x(0) = 0 , and x'(0) = 0 . ( δ(t) stands for the Dirac delta function.) Solve for x s . Possibly useful formulas: Quadratic formula: x = − b ± b 2 − 4 a c 2 a Integration by parts: ∫ a b f x g' x dx = f x g x ] a b − ∫ a b f ' x g x dx...
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This note was uploaded on 08/30/2011 for the course CGN 2200 taught by Professor Glagola during the Spring '11 term at University of Florida.
 Spring '11
 GLAGOLA

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