Find the Laplace transform of:

Question

f(t) = cos^(2)(2t)

Answer 1

cos^2(2t)

L{cos(t)} = s/(s^2+1)
L{f(at)} = 1/a f(s/a), so
L{cos(4t)} = 1/4 (s/4)/(s^2/16+1) = s/(s^2+6)

L{cos^2(2t)} = L{(1+cos(4t))/2}
= 1/2 (L{1} + L{cos(4t)})
= 1/2 (1/s + s/(s^2+16))
= (s^2+8) / (s^3+16s)

Answer 2

Thank you!!

Answer 3

L(cos^2 2t)=s^2+8/s(s^2+16)