# How to get the equation spring equation? Please help me understand!

How do you use the equations

m=Minital + deltaM
and x=xinital + deltax
and F=-mg

to get x=(g/k)deltaM + ((Minital)(g)/k +xinital)

(where m= mass. Minital is fixed inital mass and deltaM is additional weight added)
(where x= displacement. xinital is when no downward force is applied and deltax is displacement from unstretched position)

please explain how to get this equation

Thank you

## Answers and Replies

atyy
Science Advisor
It can't be done. You need one more equation: Force that the spring exerts on a mass = k * extension.

so if I use F=-kdeltax than how can I now show the above equation?

Chandra Prayaga
Science Advisor
Perhaps I can help if I understand the problem better. What was the statement of the problem? The equations can come later.

m = mi + Δm
Fg = -mg
so
Fg = -g(mi + Δm)

Fs = kΔx (positive since it is acting against gravity)

We are looking for Δx when the forces cancel so
0 = Fg + Fs
-Fs = Fg
-Fs = Fg = -g(mi + Δm) = -kΔx
devide by -k

Δx = g(mi + Δm)/k

The using x = xi + Δx
substitute Δx, multiply out and rearrange a bit and you get

x=(g/k)Δm + (g/k)mi +xi