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# Worksheets of Fourier Series and Laplace Series

Test your skills on Fourier Series and Laplace Series by trying out Fourier Series and Laplace Series worksheets. 2 Fourier Series and Laplace Series worksheets available to gain expertise and excel in your grades. The worksheets on Fourier Series and Laplace Series have been designed to offer a wide range of questions covering all details of the Fourier Series and Laplace Series and are in compliance with the k-12 curriculum. Detailed answers will be provided after you have attempted the Fourier Series and Laplace Series worksheet. Each worksheet will have around 10 questions and there are multiple worksheets available to try out.

• ## Fourier Series and Laplace Transform Worksheet

1. Find out the Laplace transform of the function given below:
f(t) = t when 0 ≤ t ≤ ( ½ )
f(t) = t – 1 when ( ½ )≤ t ≤ 1
f(t) = 0 when t > 1?
• (1/s2) [ (e-s - 1) + se(-s/2)]
• (1/s2) [ (e-s - 1) + se(-s/2)]
• (1/s2) [ (e-s - 1) + se(-s/2)]
• (1/s2) [ (e-s - 1) + se(-s/2)]
2. Find out the Laplace transform of the function f(t) = (1/t2) (1 – cos t)?
• s log s / √(s2 + 1) + tan-1 (3/s)
• s log s / √(2s2 + 1) + tan-1 (2/s)
• s log 2s / √(s2 + 1) + tan-1 (2/s)
• s log s / √(s2 + 1) + tan-1 (1/s)
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• ## Fourier Cosine Transform Worksheet

1. Find the cosine transformation for Fourier series where  function f(t) = cos (πpt)?
• f(u)   = ½ δ(u-p) + δ(u +)p
• f(u)   = ½ δ(u-p) + ½ δ(u -p)
• f(u)   = ½ δ(u-q) +  δ(u q)
• f(u)   = ½ δ(u-p) + ½ δ(u +p)
2. Find the cosine transformation for Fourier series where function f(x) = eax where interval of this function is (-π, π)?
• n = (a(-1)n sinh(aπ))/π(a2+n2)
• n = (2a(1)n sinh(aπ))/π(a2+n2)
• n = (2a(-1)n sinh(aπ))/π(a2+n2)
• n = (2(-1)n sinh(aπ))/π(a2+n2)
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