Midpoint Position Splits Energy - Waves, Oscillations, and Resonance Step by Step

At half the amplitude, spring and kinetic energy share the total.

At half the amplitude, spring and kinetic energy share the total. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Half displacement gives one-quarter spring energy

At position 2 metres, the checked spring energy is 4 joules.

U={1\over 2}\cdot 2\cdot 2^{2}=4\ \mathrm{J}

The rest of the total is kinetic energy

The total 16 joules minus 4 joules leaves 12 joules of kinetic energy.

16+(-4)=12\ \mathrm{J}