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Plotting numerical Laplace inverse transforms

I need to plot the impulse response of a strange filter:

H(s) = 1/(s * Cosh[Sqrt[s]])

I tried to brute-force it through MMA 2.0 (on a NeXT):

Plot[InverseLaplaceTransform[1/(s Cosh[Sqrt[s]]), s, t], {t, 0, 3}]

but this blew MMA's little mind. Any suggestions would be appreciated,
including a more efficient approach to the problem (I believe MMA is
doing two numerical integrations for every data point...).

Thanks in advance,

(mass at

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