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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?

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# Homework Help: Vertically driven mass against spring

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