1. First let me start by saying that there are similar posts about this, but I wasn't able to figure out what I need through those. A 3.45 kg mass vertically compresses a spring 67.0 cm before it starts to rebound. How high will the Mass move above the uncompressed if the mass is left to “bounce” back up? 2. Relevant equations mg=-kx k=-mg/x U=1/2kx^2 E(top) = E(bottom) 3. The attempt at a solution: To figure this out (or at least try to) I set the spring's neutral position as 0m and the distance from the spring's neutral up to the top of the rebound as 'd'. I also set 0.670m as 'a' to help work my way through the problem. Here's how I tried to work my way through: Energy at the bottom: K=0 U(spring)=1/2k(a^2) U(g)=mg(-a) Energy at the top: K=0 U(spring)=1/2k(d^2) U(g)=mgd Then I set the energy at the bottom equal to the energy at the top: 1/2k(d^2)+mgd=1/2k(a^2)-mg(-a) Here is how I broke that equation down: Get rid of the 1/2: k(d^2)+2mgd=k(a^2)-2mg(-a) Get rid of the k by using k=-mg/a: d^2-2ad=a^2-2a^2 Get everything on one side: d^2-2ad+a^2=0 (d-a)(d-a)=0 d=0.67 The spring has to work against gravity on the way up, does it make sense that it goes the same distance up as it was compressed?