The physics
A block on a spring swings on a smooth floor. At the ends it stops, so all its energy sits in the spring. At the centre the spring holds nothing, and all of it is kinetic.
E = ½kA² U = ½kx² K = ½k(A² − x²)
So K + U stays the same all the way. The KE graph against x is a hump, not a straight line.
From the top speed: ½mv² = ½kA². At any point, v² = ω²(A² − x²). Two points on one swing give ω.
A = vmax/ω ω² = (v₁² − v₂²)/(x₂² − x₁²) k = mω²
A sudden kick changes the speed but not x. A lump that sticks keeps the momentum. But the heavier block has a smaller ω.
A'² = x² + v'²/ω'²
Over a whole swing, the average KE and the average PE are both E/2.