# Don’t know where to start on a DE regarding a spring problem?

1. May 26, 2012

### caliboy

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

Ok here is the problem and I’m not sure on how to attack it.

"A gun on a tank is attached to a spring-mass-dashpot system with spring constant of 100α and a damping constant of 200α. The mass of the gun is 100. Assume that the displacement of the gun from its rest position after being fired at t=0 is y(t). The equation describin y(t) is:
100(d2y/dt2)+200α(dy/dx)+100α2y=0

and y(0)=0, (dy(0)/dy)=100

It is desired that one second after firing, the quantity, y2+(dy/dx)2 should be less than 0.01. How much larger must α be to guarantee this to be so?

2. Relevant equations
Laplace transform?

3. The attempt at a solution
I’m going to be honest. I have looked in math and engineering textbooks to get a handle on this problem but haven’t been very successful. I am trying to use the Laplace transform because this is a Differential Equation with respect to time (do you know of an easier method other than Laplace). Can someone point me in the right direction on solving this problem?Any suggestions would be greatly appreciated.

Last edited: May 26, 2012
2. May 26, 2012

### vela

Staff Emeritus
You have several typos in your post. It would help if you would carefully proofread and fix your post.