# Checking whether my Diff EQ limit problem is correct

figured it out, thanks

Figured it out, thanks.

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I believe I have solved the problem, I just want to make sure of its correctness.

I was to solve a spring differential equation that involved a damping force and to create a equation of motion. I did. Now, I need to figure out whether the weight ever passes through its equilibrium. The equation I ended up with is

x = e^(-8t) * (.5 - 2t) where x is displacement and t is time.

Now, to check whether weight passes through the equilibrium, what I did was set up the limit as x approaches infinity of (.5 - 2t)/(e^8t). Then, I used l'hopital's rule to find the limit as x approaches infinity of (-2)/(8e^8t). This comes out to be that the limit is 0, and therefore, the spring never passes through the equilibrium and there is no t-value.

Is my logic sound and my math correct?

I think you wrote the wrong thing. Don't you want to take the limit as t goes to infinity?

LCKurtz
Homework Helper
Gold Member
I believe I have solved the problem, I just want to make sure of its correctness.

I was to solve a spring differential equation that involved a damping force and to create a equation of motion. I did. Now, I need to figure out whether the weight ever passes through its equilibrium. The equation I ended up with is

x = e^(-8t) * (.5 - 2t) where x is displacement and t is time.

Now, to check whether weight passes through the equilibrium, what I did was set up the limit as t approaches infinity of (.5 - 2t)/(e^8t). Then, I used l'hopital's rule to find the limit as t approaches infinity of (-2)/(8e^8t). This comes out to be that the limit is 0, and therefore, the spring never passes through the equilibrium and there is no t-value.

Is my logic sound and my math correct?

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.

LCKurtz
Homework Helper
Gold Member
Right, and as t goes to infinity, it seems x gets closer and closer to x=0, but will never hit zero, is that correct or am I still lost?

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.

LCKurtz
Homework Helper
Gold Member
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.

LCKurtz