For a vertical spring, if we let [math] x_s [/math] be the total extension of the spring from its equilibrium position without a hanging object, then why does [math] x_s = -\left(\frac{mg}{k}\right) + x [/math]? Is this saying that the extension of the spring is changed for a vertical spring when a weight is added on? Does it follow from:

 

[math] -kx = mg [/math]

 

[math] x = -\left(\frac{mg}{k}\right) [/math]?

 

Why is there a [math] +x [/math] in the [math] x_s [/math] expression?

 

 

Thanks

I can't remember the equations or definitions off hand atm.

 

But from what I recall, isn't that x just the initial displacement when the spring is at rest?