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Lecture

# Second Translation Theorem.pdf

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School
Pennsylvania State University
Department
Mathematics
Course
MATH 251
Professor
Unknown
Semester
Spring

Description
Second Translation Theorem (of the Laplace transform): -cs -cs L{u (tcf(t - c)} = e  L{f(t)} = e F(s) -cs L{u (tcg(t)} = e  L{g(t + c)} Examples -cs -cs L{u (t)f(t - c)} = e  L{f(t)} = e F(s) c This is typically used in reverse. Start with e -cF(s) and follow the formula from there. -4s ▯▯▯▯▯ Find the inverse Laplace transform of: e ▯ ▯▯▯▯▯▯ -4s ▯▯▯▯▯ e ▯ ▯▯▯▯▯▯ (after partial fractions this becomes) e-4s( ▯ – ▯ ) ▯▯▯ ▯▯▯ e-4s(4e – e )-5t 2(t – 4) -5(t – 4) u 4t) (4e – e
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