Equilibrium

[racuna]

I have a lot of equations that ask me for the equilibrium position. I have no clue what that means. My teacher didn't go over that. Help?

 

[ryan_kidz]

I know only equilibrium. Equilibrium is a stable situation.

i'm not sure what your teacher meant by equilibrium position. Balance equations I guess.. u'd better ask ur teacher. I'm sure if he's a good teacher he'll explain it.

 

[racuna]

Show me equilibrium

 

[wgunther]

It would be nice to see an example problem or the equations. Only place I remember "equilibrium position" is from introductory physics about springs called Hooke's law I believe.

 

[racuna]

The Equilibrium Problem

s=cos(t)+3sin(t), t>=0

It asks, when the mass passes through the equilibrium position for the first time.
Then, how far from the equilibrium position the mass travels.

 

[Unco]

The equilibrium position is where the spring is unstretched. If s(t) is displacement from the equilibrium position, the mass passes through the equilibrium position when s(t)=0.

0 = cos(t)+3sin(t)
-3sin(t)/cos(t) = 1
-3tan(t) = 1
etc

The maximum displacement (amplitude) occurs when the velocity, ie. s'(t), is zero. So find s'(t) and set it to zero to find the time to get there, and plug t into s(t) to get the displacement