Oscillatory Case. (Differential Equations)
A 96-lb weight is hanging from a spring whose constant is 5 lb/ft. The weight is set in motion at x = 3 ft with an initial velocity of -6 ft/sec. Discuss the resulting motion if the surrounding medium offers a resistance numerically equal to four times the velocity.
m=96/32=3
r=4
k=5
r

Question

Oscillatory Case. (Differential Equations)
A 96-lb weight is hanging from a spring whose constant is 5 lb/ft. The weight is set in motion at x = 3 ft with an initial velocity of -6 ft/sec. Discuss the resulting motion if the surrounding medium offers a resistance numerically equal to four times the velocity. 
m=96/32=3
r=4
k=5
r<2sqrt(mk), so it's case III.
alpha = r/2m = 4/(2*3) = 2/3
beta = sqrt(k/m-alpha^2) = sqrt (5/3 - (2/3)^2)    = sqrt(11)/3
x=Ae^(alpha*t)cos(beta*t-delta)
Answer: sqrt(153)e^(2/3t)cos(1t/3-arctan(-4))
As you can see, my beta is not the same as the answer's..Y?