Inverse laplace and limits

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Ali Almakhmari 2020-12-8

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https://ww2.mathworks.cn/matlabcentral/answers/687118-inverse-laplace-and-limits

评论： Bjorn Gustavsson 2020-12-9

How can I find the limit as t goes to infinity of the inverse laplace function (A)? Code Below

syms s

G = (14*s^2+32)/(s*(s^2+4)*(2*s^2+3*s+8));

A = ilaplace(G)

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David Goodmanson 2020-12-9

在 MATLAB Online 中打开

Hello Ali,

A =
 sin(2*t) - exp(-(3*t)/4)*(cos((55^(1/2)*t)/4) + (55^(1/2)*sin((55^(1/2)*t)/4))/5) + 1

t-->infinity makes the term involving exp go away, but that leaves sin(2*t) +1 which does not go to a limit as t-->infinity. Life is like that sometimes.

The Final Value Theorem gives an answer of 1 which gets the constant part right, but unfortunately it only applies if there actually is a limit.

The culprit is the (s^2+4) factor, which has roots s = +-2i with no negative real part.

Bjorn Gustavsson 2020-12-9

From my use of the Laplace-transform (as a physicist) I'd take that sin(2*t)+1 as a limit-behaviour of the ODE-solution as time becomes large - and be happy with that.

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