Obtain the laplace transform of each of the following

Question

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^-2tcos(3t)u(t)

(b) e^-2tsin(4t)u(t)

(c) e^-3tcosh(2t)u(t)

(d) e^-4tsinh(t)u(t)

(e) te^-2tsin(2t)u(t)

Problem 3 - Find the inverse Laplace transform of:

V(s) = (2s + 26)/(s(s² + 4s + 13))

Problem 4 - Use the Laplace transform to solve the differential equation

dv²(t)/dt² + 2 dv(t)/dt + 10v(t) = 3 cos(2t)

subject to v(0) = 2, dv(0)/dt = -2.