Unformatted text preview: 00 + kx = f ( t ) models the movement of a mass attached to the end of spring with no dashpot. So we need to solve x 00 + 4 x = 8 δ π ( t ) , x (0) = 3 ,x (0) = 0 . Applying Laplace transform to both sides of the equation, b x 00 ( s ) + 4 b x ( s ) = 8 δ π ( s ) s 2 b xsx (0)x (0) + 4 b x ( s ) = 8 eπs ( s 2 + 4) b x ( s )3 s = 8 eπs Solve for b x ( s ), we get b x ( s ) = 3 s s 2 + 4 + 8 s 2 + 4 eπs Using Mathcad , we can ﬁnd inverse Laplace transform, x ( t ) = 2 cos(2 t ) + 4 u π ( t )sin(2 t ) = ‰ 2cos(2 t ) if 0 ≤ t < π 2cos(2 t ) + 4sin(2 t ) if t ≥ π So clearly the impact of the impulse is felt by the spring and change the its movement immediately. The solution curve is shown below, a...
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 Spring '11
 Dr.Han
 Laplace, Laplace transform methods

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