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

Maiclubk 2021-02-09 Answered
Transform:
f(t)=cos2at
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Arham Warner
Answered 2021-02-10 Author has 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)
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more