A spring of length D and constant k is hung from the ceiling. A nonstretchable string of length L is attached to the bottom of the spring. An object of mass m attached to the free end of the string and dropped from the ceiling. What is the lowest the object would reach? I'm supposed to solve this strictly using energy. No amplitude or anything like that. Here I go: E = Ug + Us Ug = (D + L)mg Us = .5kx2 That all I know about U. How do I find how far the spring stretches past its equilibrium position, when it stretches the farthest away from the point of origin? This is my guess: Since it's all potential energy at the time of release, the spring is unstretched: mg(D + L) = .5kx2 x = sqrt((2*mg(D + L))/k) So the lowest point would be D + L + x So can someone explain to me all the conceptual errors I made and how those concepts are supposed to apply in this situation? Thanks.