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muzialis

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in a previous post on the physical meaning of Laplace's Transform I found the following statement

" The fundamental Laplace transform pair is H(t), the Heaviside step function, and 1/s, its spectrum of damped sinusoids. Note that the spectrum is weighted towards low frequencies (1/abs(s) goes to zero as abs(s) goes to infinity), as one would expect for an excitation that begins but is never turned off".

I am struggling to understand where the spectrum of damped sinusoids comes from, I found this interesting.

Can anybody maybe help?

Thanks a lot