thumbnail|left|100px|Experimental Setup of Huygens synchronization of two clocks The harmonic oscillator and the systems it models have a single degree of freedom. More complicated systems have more degrees of freedom, for example, two masses and three springs (each mass being attached to fixed points and to each other). In such cases, the behavior of each variable influences that of the others. This leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks (of identical frequency) mounted on a common wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665. The apparent motions of the compound oscillations typically appears very complicated but a more economic, computationally simpler and conceptually deeper description is given by resolving the motion into normal modes.
tHuMbnAil|left|100Px|exPeRiMenTal seTuP OF hUygenS sYNchrOnization of twO clOCks thE HarmoNiC oscillaToR and the sysTeMs It modELs haVE a singLe degree Of FReedom. MoRe coMPLiCAted SYsTems hAVe More DEgreEs oF freedom, for exAMpLe, tWO massEs And ThrEe springs (each mass BeinG attaChEd tO FIxED POInts AnD TO eaCh other). In Such Cases, thE BehaVioR OF eacH vaRIable iNflUenCeS tHaT oF the oThers. This Leads to A cOuPliNg of the oScillAtIons Of the iNdividUAL dEgREES Of freEdOm. for ExaMPLe, tWo PEnDulUm cLoCks (Of iDentIcal FrequenCy) mounted on a CoMmon wall wIlL teNd To synCHrOniSe. tHis PheNOmenon WaS FirSt obsErveD by christIaAn huygens iN 1665. tHE appArEnt moTioNs Of THe cOmpound oscILLations typically apPeARs Very CoMPlIcated bUT a MorE eConOmic, cOmpuTATionAlLY siMpLER and CoNcePtuAlly deEpEr DeScrIpTIOn is givEn BY RESolvinG THe moTIon into nORmaL mOdEs.