Find the laplace transform of the following function f(t)=tu_2(t)

Brittney Lord 2020-12-24 Answered
Find the laplace transform of the following function
f(t)=tu2(t)
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Expert Answer

Asma Vang
Answered 2020-12-25 Author has 93 answers

Step 1
We apply defination of Laplace transformation. 
Step 2
There u2(t)={0if t<21if t>2
Now f(t)=tu2(t)={0if t<21if t>2
L(f(t))=0f(t)estdt
=02f(t)estdt+2f(t)estdt
=0+2f(t)estdt
=2testdt
=[testdt]22[ddttestdt]dt
=[tsest]2+1s2estdt
=2se2s1s2[est]2
=e2s(2s+1s2)=e2ss2(2s+1)
So L(f(t))=e2ss2(2s+1)

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