Equation oscillations harmonic nalokho okukushoyo ekuhloleni ubunjalo izinqubo oscillatory

Zonke Harmonics abe isibalo sezibalo. izakhiwo zabo ephawula iqoqo zibalo trigonometrical, bulukhuni kwalo kunqunywa ubunkimbinkimbi inqubo oscillatory, uhlelo izakhiwo kanye nendawo lapho kwenzeka, ngamanye amazwi, iziphi izici zangaphandle ezithinta inqubo oscillation.

Ngokwesibonelo, e izihambisimshini oscillation harmonic esivusa, esibonakala by:

- uhlamvu kuqondile;

- engalingani;

- ezihambayo nemizimba yenyama, okuyinto eyenzeka ngo-trajectory sine noma cosine njengoba umsebenzi isikhathi.

Ngokusekelwe kulezi izindawo, kungabangela harmonic oscillations equation, esesikhundleni ifomu:

x = A cos ωt noma efomu x = A isono ωt, lapho x - Ukudidiyela ukubaluleka A - ukubaluleka amplitude of oscillation, ω - Coefficient.

i equation okunjalo oscillations harmonic kubalulekile zonke oscillations harmonic, okuyinto kuxoxwa ngazo kinematics kanye Mechanics.

Inkomba ωt, okuyinto kule ifomula imile isibonakaliso imisebenzi Trigonometric, ngokuthi isigaba futhi likhomba indawo oscillating mass iphuzu ngesikhathi esithile endaweni amplitude inikezwe. Uma sicabanga iyehla iyenyuka eyindilinga ingxenye esebenzayo 2N, ke libonisa inombolo kunyakaza mechanical ngaphakathi umjikelezo isikhathi luchazwa w. Kulokhu, ezothando ka oscillations harmonic iqukethe ke njengoba i value Inkomba ye eyindilinga (isiyingi) imvamisa.

Sicabanga ezothando ka oscillations harmonic, njengoba sekuphawuliwe kakade, kungathatha izinhlobo ezahlukene, kuye ezicini eziningana. Ngokwesibonelo, nakhu inketho. Ukuze sicabangele ezothando umehluko ka khulula oscillations harmonic, omunye kufanele ucabangele iqiniso lokuthi zonke avame ukuba attenuation. Tinhlobo letehlukene oscillation, lesi simanga kuzibonakalisa ngezindlela ezahlukene: ukumisa umzimba ezihambayo, ekunqanyulweni emisebeni kumasistimu kagesi. Isibonelo elula efanekisa nokwehlisa ezingaba oscillatory, ukuguqulwa ezenzweni ukushisa amandla.

Lokhu kwesibalo ine uhlobo: d²s / dt² + 2β x ds / DT + ω²s = 0. Kulesi ifomula: s - Inani ziyaguquguquka ukubaluleka lapho ephawula izakhiwo uhlelo oluthile, β - njalo okubonisa Damping Coefficient, ω - imvamisa eyindilinga.

Ukusebenzisa lolu ifomula ivumela yokusondela incazelo oscillatory izinqubo kumasistimu komugqa ngombono owodwa, futhi ukwenza idizayini kanye sekulingisa izinqubo oscillatory ku yesayensi ezingeni zokuhlola.

Ngokwesibonelo, kuyaziwa ukuthi oscillations damped at esigabeni sokugcina zako ayeka ukuba khona harmonic, ie isigaba nobuningi isikhathi ukuba babe nje lutho futhi kuthiwa ayibonwa.

Indlela zakudala sokutadisha kunyakaza harmonic wenza oscillator harmonic. Ngendlela elula kuba uhlelo echaza ezothando umehluko oscillations harmonic: ds / DT + ω²s = 0. Kodwa ezininginingi izinqubo oscillatory iholela ngokwemvelo yokuthi kukhona inqwaba oscillators. Lapha izinhlobo ezinkulu:

- a oscillator entwasahlobo - umthwalo evamile kokuba mass m ezithile, okuyinto okwesikhashana ku-entwasahlobo nokunwebeka. It oscillates uhlobo harmonic, ezichazwe by ifomula F = - Kx.

- oscillator ngokomzimba (pendulum) - okuqinile, oscillates bezungeza-eksisi static bedle ibutho elithile;

- pendulum zezibalo (ngokwesimo cishe ingekho). Kuyinto enhle imodeli uhlelo ehlanganisa umzimba oscillating ngokomzimba kokuba mass ezithile, okuyinto okwesikhashana kwi izindikimba eqinile nakho ngeke kusize awunzima neze.