What are practical applications of Laplace Transforms in the real world

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In lay man's terms what really in the real world are practical examples of how Laplace transforms are used to solve basic mathematical problems in mechanical engineering I would really appreciate a very simple and clear answer with less mathematical jargon plus a few examples.

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If you were an electrical engineer the practical (and very useful) applications of the Laplace (Fourier) transform would be very clear.
That is, in crude words as you require, the study of the response of a system to solicitations of different frequencies and how to cope with them.

The Bode and Nyquist plots are paradigmatic.

In the mechanical field that finds application in the study of vibrations especially, which means resonance phenomena, acoustic noise, fatigue and so on.