A simple pendulum of length and mass has its support point moving horizontally in a sinusoidal manner x = a * sin(wt) where a and w are constants. Determine the equations of motion.

a. ddot θ + (g/b) sin θ - (a/b) sin (ωt) cos θ = 0
b. ddot θ + (g/b) sin θ - (a/b) ω² sin (ωt) cos θ = 0
c. ddot θ + (g/b) sin θ - (a/b) sin (ωt) = 0