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When we find the solution of a system using the Laplace transform, it gives a complete solution unlike the differential equation approach which gives the transient part the steady state part separately. Is there a way we can identify which part constitutes the transient part using the Laplace transform? (Mathematically?)

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  • \$\begingroup\$ When you convert a "block" to Laplace there is no implied transient nor steady-state part. That only comes when you multiply the Laplace transform of the "block" with your desired input waveform (in Laplace form). So, what are you actually asking. \$\endgroup\$
    – Andy aka
    Jun 10, 2021 at 12:29
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    \$\begingroup\$ The Laplace solution and the differential equation solution must be exactly the same. You don't get a different system by analysing it in different ways. \$\endgroup\$
    – Chu
    Jun 10, 2021 at 21:19

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The solution of a linear system should contain some exponential terms which decay towards zero when time grows towards infinity. Let those exponentials be zero. What's left, that's your steady state response.

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