Damping isaterm fordescribingthe lossesofanoscillatorysystem(see Fig. 1 and left panel of Fig. 2). The losses can be internal,molecular friction (dissipation, causing generation of heat) and/ortransmission to the surrounding elements, e.g., through the bridgeandbodyofastring instrument tosoundwaves in thesurroundingair.

Figure 1: Example of amplitude reduction due to losses(damping).Here, the frequency is10Hz,and theQvalue10,which implies that theamplitudehas fallen toabout4.3%oftheinitialamplitudeafteronesecond.

Thereare,however,anumberofexpressionsfordamping,allwithaparticular mathematical meaning. (Unfortunately, with wordssounding somuchalike,wecan seesome inconsistencyalsowithinthe scientific society.) In the following these expressions will bedefinedasfunctionsofQvalue(seeentryQvalue),andT60,wherethelatterisameasureofhowlongittakes(inseconds)toreducetheoscillationwith 60 dB (i.e., to onemillionth of the energybarelyaudible,ifatall).

Loss factor (commonlyusedsymbol:, dimensionless) is the inverseoftheQvalue:

=1/Q2.2/(T60f0),wheref0istheoscillatoryfrequency.Decay ratio (not to confuse with radiometric dating), (commonlyusedsymbol:D, dimensionless)isequaltohalfthevalueof:

D =1/(2Q)1.1/(T60f0).Decay constant (commonly used symbol: , with dimension: persecond,[s1]):

= f0/Q 6.9/T60.Logarithmicdecrement(commonlyusedsymbol: , dimensionless): = /Q 6.9/(T60 f0).Damping coefficient is here the viscous damping coefficient, i.e.,mechanical resistance, realizableasadashpot, (commonlyusedsymbol: c,withdimension[kg/s]=[Ns/m]): c=2 f0 mass/Q13.8 mass/T60.

Whentheterminologyoftheseexpressionsissoeasilyconfusable,onemight askwhy there are somany terms. The answer is that one cansignificantlysimplifyequationsbychoosingthemostsuitableone,andwhenenteredintoequations,thecontextusuallydefinesthemclearly.Thereare,however,threemoreexpressionsyoushouldbeawareof:Overdamping,Criticaldamping,andUnderdamping(seeFig.2).

Figure 2: Examples of different degrees of damping:Overdamped,Criticallydamped,andUnderdamped(seetext).

When something resonates, the three elements shown at the leftsideofFig.2willbepresentinoneformoranother.Wecanimaginethatthemassisatrestfirstinequilibriumwiththeattachedspring.Then,attime=0,theupperendofthespringisinstantlybroughttoahigher level, being stretched,whichwill cause themass to follow.Dependentonthe levelofdamping (viscousresistance)providedbythedashpot,thepositionofthemassmightnowdescribeadampedsinewave, overshooting the new equilibrium level at first, beforegraduallysettlingatitsnewequilibriumlevel(seeredlineintherightpanel of Fig.2). This is called underdamping, and is present in allinstruments with soundboards and vibrating walls. (Without thedissipating dashpot effect, the sine wave would go on forever,undamped.)

Atacertainhigherlevelofdamping,themasswillnotovershoot,butfind its approximate new position within a little more than onenominal period of the underdamped or undamped oscillationfrequency (which is primarily dependent on the springmass ratio).This,beingthequickestwayofgettingfromlevel0tolevel1withoutovershooting,iscalledcriticallydamped(seeblacklineofFig2).

If the dashpot resistance is increased even further, the system isgetting overdamped, and the transition will take longer thannecessary (see blue line of Fig. 2). In elevators, the damping isusuallyoverdampedtoavoidringing(theeffectofoscillationafterthe chosen level is reached) and to give a soft landing at yourdestination.