Start with Ebefore = Eafter to derive the maximum velocity in a spring SHM system

Question

Start with Ebefore = Eafter to derive the maximum velocity in a spring SHM system

Answer 1

While I've drawn the system in the horizontal direction, the same approach applies to a vertical system, the difference being that Δx would then be the displacement from the rest position (e.g. the position where the the mass rests under it's own weight) rather than the change in the length of the spring from it's unstressed length.