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Alice sent it to me in pdf form.

for part b, the homogenous solution is different depending on if b^2-4ac is less than zero. i have the discriminant being (.5+ki)^2-4kp(1+kd). do we assume that this is greater than zero and the homogenous solution is cexp(rt) or do we assume it is less than zero and the solution is exp(rt)(cos(n*t)+sin(n*t))?

nloyd wrote:for part b, the homogenous solution is different depending on if b^2-4ac is less than zero. i have the discriminant being (.5+ki)^2-4kp(1+kd). do we assume that this is greater than zero and the homogenous solution is cexp(rt) or do we assume it is less than zero and the solution is exp(rt)(cos(n*t)+sin(n*t))?

That doesn't matter if all you are concerned about is stability. It's the real part of the root that determines stability. The imaginary part just determines the frequency of the oscillations.