# Homework Help: Maximum speed of overdamped oscillator without crossing origin

1. Oct 3, 2012

### MeMoses

1. The problem statement, all variables and given/known data
An overdamped oscillator with natural frequency w and damping coefficient g starts out at postion x0 > 0. What is the maximum initial speed towards the origin it can have without crossing the origin?

2. Relevant equations
x(t) for overdamped oscillator

3. The attempt at a solution
x(t) for a general overdamped oscillator has been solved already. However if I only know x0 > 0 and nothing else, how do I go about determining the maximum speed. I can't see how this problem will workout and I can't get it started. Thanks for any help

2. Oct 3, 2012

### tiny-tim

Hi MeMoses!
Just find the answer as a function of xo

3. Oct 3, 2012

### MeMoses

Edit: My idea made no sense. So how do find this maximum v0?

Last edited: Oct 3, 2012
4. Oct 3, 2012

### tiny-tim

what is your x(t) equation?

5. Oct 3, 2012

### MeMoses

I get x(t) = Ae**((-g-z)t) + Be(-(g-z)t) with z=sqrt(g**2 - w**2). At t=0 I get x0 = A + B

Last edited: Oct 3, 2012
6. Oct 3, 2012

### tiny-tim

Hi MeMoses!
(hmm … i'm not sure how that's supposed to be read … but anyway …)

So what is the maximum value of x(t) (presumably at t = ∞) ?

And what is the intitial speed?

7. Oct 3, 2012

### MeMoses

Sorry i type that from my phone. The lim x(t) as t approaches infinity is 0, it will always go to 0 eventually but how do I know if it crosses the origin or not and how can I find the initial speed using what you told me? Edit: also how can I solve the coefficients?

Last edited: Oct 3, 2012
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