θ = .5e-3πtcos4πt
ω = dθ/dt = .5(-3πe-3πtcos4πt - 4πe-3πtsin4πt)
α = dω/dt = .5(9π2e-eπtcos4πt + 12π2e-3πtsin4πt + 12π2e-3πtsin4πt - 16π2e-3πtcos4πt)
= .5(24π2e-3πtsin4πt - 7π2e-3πtcos4πt)
A) at t=0
θ = .5 rad
ω = .5*-3π = -4.71 rad/s
α = .5*-7π2 = -34.5 rad/s2
B) at t = .125s
e-3πt = .30786
θ = .5*.30786*0 = 0
ω = .5*.30786*-4π = -1.93437 or -1.934 rad/s
α = .5*.30786*24π2 = 36.461
α = 36.5 rad/s2