# 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 ${\displaystyle {\vec {F}}}$ 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 (${\displaystyle L_{0}}$) equals ${\displaystyle \lambda /4}$, where ${\displaystyle \lambda }$ 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.