A Bromwich contour is a vertical line in the complex frequency plane lying to the right of the singularities in the inverse Laplace integral.
When an inverse Laplace integrand contains on the principal branch, closing the Bromwich contour to the left encloses isolated poles and wraps a branch cut along the negative real axis. Pole residues give persistent oscillatory terms, while the jump across the two sides of the cut gives a real decaying integral.
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