Lissafi masu jituwa oscillations da muhimmanci a binciken da yanayin oscillatory matakai

All harmonics da ilmin lissafi magana. Dũkiyõyinsu characterizes sa na trigonometrical lissafai, haduwar wanda aka ƙaddara da wuya daga cikin oscillatory tsari, tsarin da kaddarorin da kuma yanayin da suke faruwa, Ina nufin, da waje dalilai da shafi cikin oscillation tsari.

Alal misali, a cikin makanikai da masu jituwa oscillation ne mai motsi, wanda aka halin:

- saukin ganewa hali.

- m.

- motsi jiki jikinsu, wanda ya auku da wani ba tare da ko cosine yanayin a matsayin aiki na lokaci.

Bisa ga wadannan kaddarorin, zai iya sa masu jituwa oscillations lissafi, wanda yana da siffar:

x = A cos ωt ko siffar x = A zunubi ωt, inda x - daidaita darajar A - tamanin da mawadãta daga oscillation, ω - coefficient.

Irin wannan lissafi na masu jituwa oscillations yana da muhimmanci ga duk masu jituwa oscillations, wanda aka tattauna a cikin kinematics da makanikai.

Nuna alama ωt, wanda a cikin wannan dabara tsaye ga alama na trigonometric ayyuka, da ake kira zamani, kuma tana nuna da wuri daga cikin oscillating taro batu a iyakancen lokaci a wata ba mawadãta. A lokacin da la'akari da cyclic hawa da sauka aiki bangaren shi ne 2n, shi ya nuna da yawan inji vibrations a cikin lokaci sake zagayowar da aka denoted w. A wannan yanayin, da lissafi na masu jituwa oscillations ƙunshi shi a matsayin index darajar da cyclic (madauwari) mita.

Muna la'akari da lissafi na masu jituwa oscillations, kamar yadda muka rigaya muka gani, zai iya daukar daban-daban iri, dangane da dalilai da dama. Alal misali, a nan ne wani zaɓi. Don la'akari da bambanci lissafi na free masu jituwa oscillations, daya ya kamata la'akari da cewa su duka ayan attenuation. A daban-daban na oscillation, wannan sabon abu bayyana kanta a hanyoyi daban-daban: dakatar da wani dabba ba a kanta jiki, da radiation karewa a lantarki da tsarin. A sauki misali dake bayyana akan rage oscillatory m, ta hira cikin zafin rana makamashi ayyukan.

Wannan lissafi yana da siffar: d²s / dt² + 2β x DS / dt + ω²s = 0. A wannan dabara: s - darajar fluctuating darajar wanda characterizes da kaddarorin wani musamman tsarin, β - m nuna wani damping coefficient, ω - cyclic mita.

Amfani da wannan dabara damar da tsarin kula da bayanin oscillatory matakai a mikakke tsarin daga guda ra'ayinsa, da kuma yin zane da kuma kwaikwaiyo na oscillatory matakai a kan kimiyya gwaji matakin.

Alal misali, an san cewa damped oscillations a karshe mataki na ta bayyananen gushe zama masu jituwa, watau category na mita da kuma lokacin su zama kawai m da kuma da'awar an ba a gane.

The classic hanya domin karatu masu jituwa vibrations aikin masu jituwa oscillator. A cikin sauki form shi ne wani tsarin wanda ya bayyana a bambanci Jadawalin masu jituwa oscillations: DS / dt + ω²s = 0. Amma da yawa oscillatory matakai take kaiwa ta halitta ya nuna gaskiyar cewa akwai babban adadin oscillators. A nan suna da babban iri:

- wani spring oscillator - al'ada kaya da ciwon wasu taro m, wanda aka dakatar a kan wani na roba spring. Yana oscillates masu jituwa irin, wanda aka bayyana da dabara F = - kx.

- jiki oscillator (Pendulum) - m, oscillates a kusa da wani a tsaye axis a ƙarƙashin rinjayar da wani karfi;

- ilmin lissafi Pendulum (a cikin yanayi kusan ba ya faruwa). Shi ne manufa model tsarin kunsha na oscillating jiki jiki da ciwon wasu taro, wanda aka dakatar a kan wani m weightless zaren.