## Seperation constant giving a harmonic dependence. (Seperation of variables)

1. The problem statement, all variables and given/known data

3. The attempt at a solution
I'm on part b) where it asks which seperation constation gives a harmonic time dependence. From part a) I deduced the equation $\frac{d^{2}T}{dt^{2}}$$\frac{1}{T}$ = a constant. I'm choosing the constant $k^{2}$ and my question is does it matter if the constant is negative or positive? I have seen in textbooks that a positive constant gives the solution T(t) = Aexp(-kt) + Bexp(kt) whereas a negative one would be Acos(kt) + B sin(kt). Are both solutions equivalent or does only one of them give a harmonic time dependence (My guess would be the sin/cos one is the proper answer for this question.)
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