Physics/A/String vibration/Energy (simple)

The circles are touching where the spring is in its relaxed state. Compression (expansion) is illustrated with circles that are overlapping (spaced-apart). At low frequency the motion is the distortions are uniform over the length of the spring, with the force ${\vec {F}}$ at the end being equal to the uniform tension in the spring. The ultimate breakdown occurs when the frequency is increased to the point where the the spring's relaxed length ($L_{0}$) equals $\lambda /4$, where $\lambda$ is the wavelength of a compressional wave associated at the driving frequency. At this point the end of spring is an antinode of the motion, and consequently oscillates with a driving force equal to zero.

An asserted fact.

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Another asserted fact.

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A third asserted fact.