The enhanced vibrations in the individual hacksaw blades demonstrate how the precise matching of two oscillating systems transmits a maximum amount of energy. We will now summarize what we have seen so far with an explanation of the energy transfer that occurs at resonance. A mass, m, attached to a spring. The minus sign indicates that the restoring force is always opposite to the direction of displacement from its equilibrium position. This is very similar to the period of oscillation of a pendulum where g , the acceleration due to gravity, serves as a measure of the restoring force, as k does in our oscillation mass.
Large amplitudes occur when the driving force is in phase with the natural vibration of the system.
The energy of the driving force appears as vibrational energy in the absence of frictional forces. When driving frequencies other than the resonant frequency are applied, the system fails to build up larger oscillations. A response curve for a driven harmonic oscillator. The final activity in this section involves an application of resonance. Matching the frequencies of tuning forks to the natural vibrational frequencies of an air column allows one to measure the resonant length of a tube in different media.