Theory

Components in a vibrating system have three properties of interest. They are: mass (weight), elasticity (springiness) and damping (dissipation). Most physical objects have all three properties, but in many cases one or two of those properties are relatively insignificant and can be ignored (for example, the damping of a block of steel, or in some cases, the mass of a spring).

The property of mass (weight) causes an object to resist acceleration. It also enables an object to store energy, in the form of velocity (kinetic) or height (potential). The property of elasticity enables an object to store energy in the form of deflection. A common example is a spring, but any piece of metal has the property of elasticity.. The size of the deflection depends on the size of the applied force and the dimensions and properties of the piece of metal. The amount of deflection caused by a specific force determines the "spring rate" of the metal piece. The resonant frequency of a system (symbolized "ω _n", pronounced "omega-sub-n") is determined by both the mass properties and the elasticity properties of the system.If you increase the mass property or decrease the elasticity property of a system, the resonant frequency will decrease according to the relationship :

where "K" is the appropriate elasticity value (spring rate) and "m" is the appropriate mass value. Note that damping has no effect on the system resonant frequency. Damping simply dissipates energy from a vibrating system, and thereby limits the amount of energy which can feed back into the system, and so limits the amount of "out-of-control" vibration which can occur near resonance. A waveform is a pictorial representation of a vibration. The term frequency occurs often in the discussion of vibration. The frequency of a waveform (torque variation, in this case) is the number of times per second that the waveform repeats itself, while the order of a waveform is the number of times that the waveform repeats itself during a particular event (such as one revolution of a crankshaft).