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(A) Whats is the extension of the spring when it is as equilibrium

0 = mg - T

0 = 2*9.8 -4x

x = 4.9m

(B) Using Newton's law of motion, derive the differential equation for the displacement of the mass y(t) below the equilibrium position. Use the downward direction as the positive direction.

ma = weight + external force - T - air resistance(ky')

i worked this out to be:

y'' + (k/9.8)x' + (4/9.8)x = 2sin(2t)

(C) For what values of the damping constant is the motion: under damped, critically damped, over damped.

This is where I'm stuck, i thought that it might have something to do with the discriminant being = 0, greater then 0 or less then 0. Any help would be greatly appreciated!