1. The problem statement, all variables and given/known data A mass m is attached to a spring of stiffness k. The spring is attached to the ceiling and the mass hangs freely from the spring under the force of gravity. (a) Derive the equation of motion for this system. (b) Find an expression for the equilibrium position of the mass ( in terms of the equilibrium position in the absence of gravity). (c) Show that the equation of motion is equivalent to the mass plus spring system in the absence of gravity. 2. Relevant equations F = -kx, Euler Lagrange equation and L = T - V 3. The attempt at a solution So for (a), I attempted to use the Lagrangian method. Taking the only degree of freedom as up and down (y direction), my velocity vector is v = dy/dx times the unit vector y hat. So T (kinetic energy) = 0.5m (ydot)^2 where y dot = dy/dx So now I need V and this is where I am confused, don't I have two potentials here; gravity and the spring potential? Which one should I take? I am guessing that I cannot take both?