This is the best video I have found that explains and uses the 2nd TT with a practical example. And its not too easy or insanely difficult, so you really get the idea of how to use it. Thank you so much man, u rock
Given: 3*cos(t)*u(t - pi) When multiplying a function g(t) by the unit step function shifted by a distance of c to the right, u(t - c), the corresponding Laplace transform is: G(s)*e^(-c*s) This means the given function's Laplace transform will be: L{3*cos(t)} * e^(-pi*s) Now we just need to find L{3*cos(t)}. Since the Laplace transform is a linear operator, we can pull the 3 out in front, and get: 3*L{cos(t)}. The Laplace of cos(t) we an look up directly, which is s/(s^2 + 1). Construct all of the above to get the solution: [3*s/(s^2 + 1)]* e^(-pi*s)
