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February 1st, 2016, 12:30 AM   #1
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Simple harmonic motion damping Laplace transform help!

Ok guys, so I'm really confused as why in the second order homogenous equation of
mx”(t) + cx’(t) + kx(t) = 0
where m = mass, c = drag coefficient, and k = spring constant
the Laplace transform of L{x(t)} = s L{X(t)}
Why isn't it L{x(t)} = s L{X(t)} - X(0)?
Where exactly did the "- X(0)" go?
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February 1st, 2016, 11:45 AM   #2
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$\displaystyle x(0)=0$
(x) equals 0 for time=0
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