Questions -
Problem 1 - Determine the Laplace transform of:
(a) cos(ωt + θ)
(b) sin(ωt + θ)
Problem 2 - Obtain the Laplace transform of each of the following functions:
(a) e^{-2t}cos(3t)u(t)
(b) e^{-2t}sin(4t)u(t)
(c) e^{-3t}cosh(2t)u(t)
(d) e^{-4t}sinh(t)u(t)
(e) te^{-2t}sin(2t)u(t)
Problem 3 - Find the inverse Laplace transform of:
V(s) = (2s + 26)/(s(s^{2} + 4s + 13))
Problem 4 - Use the Laplace transform to solve the differential equation
dv^{2}(t)/dt^{2} + 2 dv(t)/dt + 10v(t) = 3 cos(2t)
subject to v(0) = 2, dv(0)/dt = -2.