Please help! Im not sure which is the correct theory to use for this problem. A mass 1kg is driven vertically upwards against a spring. The spring has no initial compression and a spring rate of 400N/m. The mass will reach a height of 0.180m. What is the input energy if ideal conditions are assumed here. I have been given the formula E=mgS+kS², but do not understand why simply adding : E(gravity)=mgS and E(spring)=½kS² do not give me the same value. Further to this, what would be the effect of adding preload to the spring?