find Laplace transformation of the given function. L(sin(h)5t cdot cos t)

mattgondek4

mattgondek4

Answered question

2021-09-09

find Laplace transformation of the given function
L(sin(h)5tcost)

Answer & Explanation

lamanocornudaW

lamanocornudaW

Skilled2021-09-10Added 85 answers

Step 1
In the question above we have to find Laplace transformation of the given function.
Step 2
Lets L[sin(h)5tcost]=F(s)(1)
we know that sinh(5t)=(estest2)
sinh(at)=eateat2
Now put sinh(5t) value in equation (1)
=L[(estest2)cost]
=12L[estcostestcost]
we know that
L[cosat]=ss2+a2
L[eatf(t)]=F(sa),L[eatf(t)]=F(s+a)
let`s L[cost]=F1(s)
=12L[F1(sa)F1(s+a)]  a=5
=12[sa(sa)2+25s+a(s+a)2+25]
=12[s5(s5)2+25s+5(s+5)2+25]
=12[s5s210s+25+25s+5s2+10s+25+25]
=12[s5(s210s+50)s

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