Question

Make up two functions  f 1 and f2 that have the same Laplace transform. Do not think...

Make up two functions  f 1 and f2 that have the same Laplace transform. Do not think profound thoughts.

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Homework Answers

Answer #1

Let,

Then,

Thus, we have given two distinct functions whose Laplace transforms are the same.

KEY NOTES:

Definition: Let f(t) be defined for t ≥ 0. The Laplace transform of f(t), denoted by F(s) or L{f(t)}, is an integral transform given by the Laplace integral:

Provided that this (improper) integral exists, i.e. that the integral is convergent.

For functions of t continuous on [0, ∞), the above transformation to the frequency domain is one-to-one. That is, different continuous functions will have different transforms.

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