figured it out, thanks
Figured it out, thanks.
I think you wrote the wrong thing. Don't you want to take the limit as t goes to infinity?
No, your logic isn't sound, assuming your solution for x is correct. Presuming the equilibrium position is x = 0 the question is asking whether that happens for t > 0.
It isn't asking you about the limit as t goes to infinity. It is asking whether there are any finite values of t where x hits the equilibrium position.
Stop with the infinitely large bit. The question has nothing to do with infinity. The question is whether x = 0 for any value of t. It isn't a rocket science question. Look at your equation.
You're welcome. The point of questions like that is that it depends on the damping. If the system is damped strongly enough it might just ooze down towards equilibrium. Otherwise it might do as in this problem, cross equilibrium once and settle towards equilibrium. Or if it is underdamped, it might oscillate around equilibrium as it settles.
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