Section 24.5
Laplace (Higher Order)
Transforming derivatives into algebraic powers of s generalizes perfectly.
1
Introduction
Just like , higher derivatives follow a pattern.
2
General Derivative Formula
The Pattern
3
Worked Examples
Example 1: 3rd Order IVP
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Inverse using Partial Fractions.
Example 2: 4th Order Beam
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Often used for beams with point loads (Dirac deltas).
Example 3: Discontinuous Forcing
Laplace is ideal for .
Just add to the RHS.
Variation of parameters would be a nightmare here.
4
Practice Quiz
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