1. The problem statement, all variables and given/known data A block of mass, m, is dropped from height, h (above the plate), onto a plate of mass, M, which is attached to a spring with spring constant, k. The block sticks to the plate and the system starts to oscillate. What is the amplitude of the oscillations. 2. Relevant equations Etotal=K + Ugravitational + Uspring Uspring=0.5kx2 K=0.5mv2 Ugravitational=mgh Conservation of Energy 3. The attempt at a solution I decided to approach this problem from an energy perspective, setting the equilibrium position of the spring (w/ plate) as 0 gravitational potential energy. The initial gravitational potential energy is Ug=mgh. Just before it hits the plate, all of this gravitational PE is converted to KE. mgh = 0.5mv2 v= (2gh)0.5 The problem specifically states that the block "sticks" to the plate, suggesting a completely inelastic collision. I can use the conservation of momentum to find the velocity after the collision; after the collision, the velocity of the plate and block is: vf= m(2gh)0.5 / (m+M) The kinetic energy of the system is now: 0.5(m+M)vf2 = Kf The spring will then be compressed from its equilibrium position until the velocity of the plate/block becomes zero, which is the max compression/amplitude. At this point, all of the kinetic energy has been converted to elastic potential energy. 0.5(m+M)vf2 = 0.5kx2 I can then plug in my equation for vf and solve for x, which is the maximum compression/amplitude. Is this approach okay? Did I make any incorrect assumptions? Thaaaaaanks!