Find the Laplace transforms of the given functions. displaystyle g{{left({t}right)}}={4} cos{{left({4}{t}right)}}-{9} sin{{left({4}{t}right)}}+{2} cos{{left({10}{t}right)}}

opatovaL 2021-02-21 Answered
Find the Laplace transforms of the given functions.
g(t)=4cos(4t)9sin(4t)+2cos(10t)
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Dora
Answered 2021-02-22 Author has 98 answers
Step 1 : Introduction
Given function is,
g(t)=4cos(4t)9sin(4t)+2cos(10t)
We have to evaluate the Laplace transform of given function g(t)
step 2
g(t)=4cos(4t)9sin(4t)+2cos(10t)
using Laplace transform properties
L{sinat}=as2+a2
L{cosat}=ss2+a2
Applying Laplace transform on g(t) function
L{g(t)}=L{4cos(4t)9sin(4t)+2cos(10t)}
L{g(t)}=4L{cos(4t)}9L{sin(4t)}+2L{cos(10t)}
=4(ss2+42)9(4s2+42)+2(ss2+102)
=4ss2+1636s2+16+2ss2+100
Thus , Laplace transform of given function g(t) is
L{g(t)}=4ss2+1636s2+16+2ss2+100
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