Normal modes of a system of springs

[TheGreatEscapegoat]

I'm looking at what should be just a simple spring system where four identical springs are holding up a square, load-bearing pallet plate in a warehouse. Now, someone says the equation of motion for the vertical normal mode of vibration is simply d²z/dt₂ = -4(k/m)z.
Right away however, I see no gravity in this equation, I think it should be d²z/dt² = -4(k/m)z + g. Which one is right?

Also where is the LaTex editor here?

 

[mfb]

It depends on where you want z=0 to be. At the point of zero spring tension? You need your equation. At the point of equilibrium? You need the former equation.

Also where is the LaTex editor here?

Just put it in double $ or double # (inline).
##\int x^2 dx## -> $\int x^2 dx$

 

[TheGreatEscapegoat]

Alright good to know, thank you.