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Laplace Transform and Inverse Laplace Transform

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Laplace Transform and Inverse Laplace Transform

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Questions and Answers

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

(s - 3)/((s - 3)^2 + 25)

s/(s^2 + 9)

(s + 3)/((s + 3)^2 + 25) (correct)

s/(s^2 + 25)

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

exp(-a*s) (correct)

exp(a*s)

s/a*exp(-a*s)

s*exp(-a*s)

What is the Inverse Laplace transform of the function F(s) = 1/(s^2 + 4)?

cos(2t)

sin(2t) (correct)

e^(-2t) sin(2t)

e^(2t) sin(2t)

What is the Laplace transform of the function f(t) = t*u(t - a)?

exp(-a*s)/s^2 Signup and view all the answers

What is the Laplace transform of the function f(t) = e^(at) sin(bt)?

b/(s^2 + (a + s)^2 + b^2) Signup and view all the answers

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

A surface above the s-plane Signup and view all the answers

What is the Inverse Laplace transform of the function F(s) = (s - 3)/(s^2 + 4)?

e^(-3t) sin(2t) Signup and view all the answers

What is the Laplace transform of the unit step function u(t - a)?

exp(-a*s)/s Signup and view all the answers

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

(a + s)/((a + s)^2 + b^2) Signup and view all the answers

What is the Inverse Laplace transform of the function F(s) = 2/(s^2 + 4)?

2*sin(2t) Signup and view all the answers