Explain First Shift Theorem & its properties?

sagnuhh 2020-11-05 Answered
Explain First Shift Theorem & its properties?
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nitruraviX
Answered 2020-11-06 Author has 101 answers
Step 1
First Shift Theorem:
If L{f(t)}=F(s), then L{eatf(t)}=F(sa)
The proof of the First shift theorem follows from the definition of Laplace transform. It is known that,
L{f(t)}=0estf(t)dt
Step 2
Then,
L{eatf(t)}=0eatestf(t)dt
=0e(as)tf(t)dt
=0e(sa)tf(t)dt
=F(sa)
Thus, if the Laplace transform of function f(t) is known, then we can find the Laplace transform of eatf(t) using First shift theorem.
Step 3
For example,
It is known that, L{sin3t}=3(s2+9)
Then,
L{e2tsin3t}=3(s2)2+9 by first shift theorem.
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