Laplace Transform for ODEs
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Questions and Answers

What is the Laplace transform of the function f(t) = e^(-3t)cos(5t)?

  • s/(s^2 + 9)
  • 5/(s^2 + 25)
  • 3/(s^2 + 9)
  • (s + 3)/((s + 3)^2 + 25) (correct)

    • What is the Laplace transform of the Heaviside's function u(t-a)?

  • 1/(s-1)
  • 1/(s+a)
  • e^(-as)/s (correct)
  • e^(-at)/s

    • What is the Laplace transform of the Dirac delta function δ(t-a)?

  • 1/(s+1)
  • e^(-at)
  • e^(-as) (correct)
  • 1/(s-a)

    • What is the Laplace transform of the piecewise function f(t) = t, 0 < t < 1, and f(t) = 0, t ≥ 1?

    <p>e^(-s)/s</p> Signup and view all the answers

    What is the Laplace transform of the function f(t) = e^(-2t)sin(3t)?

    <p>3/(s^2 + 9)</p> Signup and view all the answers

    What is the Laplace transform of the Heaviside's function u(t-2)?

    <p>e^(-2s)/s</p> Signup and view all the answers

    What is the Laplace transform of the Dirac delta function δ(t-π/4)?

    <p>e^(-πs/4)</p> Signup and view all the answers

    What is the Laplace transform of the piecewise function f(t) = t, 0 < t < 2, and f(t) = 2, t ≥ 2?

    <p>2e^(-2s)/s</p> Signup and view all the answers

    What is the Laplace transform of the function f(t) = e^(2t)cos(4t)?

    <p>2/(s^2 + 16)</p> Signup and view all the answers

    What is the Laplace transform of the Heaviside's function u(t-3)?

    <p>e^(-3s)/s</p> Signup and view all the answers

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