Laplace Transforms

1. Find the Laplace transforms of the given functions:

View Video Solutions
  1. \( f(t) = 2e^{-3t} + 1 + t^2 \)
  2. \( f(t) = 4\sin(\sqrt{3}t) - 7\cos(5t) \)
  3. \( f(t) = \sinh(3t) - 7\cosh(5t) \)
  4. \( f(t) = \sin(3t) - e^{3t}\sin(3t) \)

2. Find the Laplace transform of the following functions:

View Video Solutions
  1. \( f(t) = 2t^3 - 3t^2 - 5 \)
  2. \( f(t) = e^{-5t} + \cos(\sqrt{2}\, t) \)
  3. \( f(t) = \sin(t/2) - \sinh(2t) \)

3. Find the Laplace transform of each of the following functions:

View Video Solutions
  1. \( f(t) = t e^{3t} \)
  2. \( f(t) = t\cos(2t) \)
  3. \( f(t) = t^2\sin(3t) \)