Transform: displaystyle f{{left({t}right)}}={{cos}^{2}{a}}{t}

Maiclubk

Maiclubk

Answered question

2021-02-09

Transform:
f(t)=cos2at

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-02-10Added 102 answers

Step 1
The function is f(t)=cos2at
Use the identity cos2x=1+cos2x2
Rewrite the function in a linear form.
f(t)=1+cos(2at)2
=12+12cos(2at)
Step 2
Use to following Laplace transformations.
L{1}=1s
L{cos(kt)}=ss2+k2
Determine the Laplace transformation.
L{cos2(at)}=12L{1}+12L{cos(2at)}
=12(1s)+12ss2+(2a)2
=12(1s+ss2+4a2)
=12(s2+4a2+s2s(s2+4a2))
=12(2s2+4a2s(s2+4a2))
=s2+2a2s(s2+4a2)

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