Mukana wokuti vanhu vanga harmonic oscillations aro kukosha kudzidza yezvakaita oscillatory pezvakaitwa

All harmonics vane kwemasvomhu mashoko. ehupfumi dzavo inechirevo akaisawo trigonometrical equations, kunzwisisa zvakatemwa kubudikidza i.e. kunzwisisa kwakaita oscillatory muitiro, maitiro zvivako uye zvakatipoteredza iyo zvaitika, kuti kwokunze zvikonzero kukanganisa oscillation rikurumidze.

Somuenzaniso, mune hurongwa ose harmonic oscillation riri sangano, icho kunoratidzwa:

- rakananga hunhu;

- gogonera;

- vatama miviri kunoitika kubudikidza sine wave kana cosine trajectory ave kushanda nguva.

Pachishandiswa ehupfumi izvi, anogona kukonzera harmonic oscillations mukana wokuti vanhu vanga, chine chimiro:

x = A Kosi ωt kana chimiro x = A chivi ωt, apo X - batanidza ukoshi A - kukosha amplitude ose oscillation, ω - coefficient.

Yakadaro mukana wokuti vanhu vanga vane harmonic oscillations kunokosha vose harmonic oscillations, izvo inokurukurwa kinematics uye hurongwa.

Chakarurama ωt, izvo mutoo uyu amire kuti chiratidzo trigonometric mashandiro, akadana danho uye rinoratidza nzvimbo oscillating vakawanda pfungwa pane imwe nguva pane imwe amplitude. Kana kukurukura cyclic nokufamba vanoshingaira zvinoriumba riri 2n, zvinoratidza uwandu zvemaziso vibrations mukati nguva kutenderera uye runotaurwa W. Panyaya iyi, mukana wokuti vanhu vanga vane harmonic oscillations rine sechiratidzo indekisi Kukosha cyclic (dzeraundi) maitikiro.

Tiri kufunga mukana wokuti vanhu vanga vane harmonic oscillations, sezvo dzatoona, anogona kutora siyana, zvichienderana zvinoverengeka. Somuenzaniso, pano nezvechisarudzo. Kutarisa kuti differential mukana wokuti vanhu vanga chokuzvisarudzira harmonic oscillations, mumwe anofanira kufunga chokwadi kuti zvose zvinoodza attenuation. Nemarudzi akasiyana-siyana oscillation, chiitiko ichi kunooneka pacharo nenzira dzakasiyana: kumisa kubvongodzwa muviri, kuti mwaranzi kugumiswa mune magetsi gadziriro. A nyore muenzaniso pokuenzanisira rutapudzo pamusoro oscillatory kwaniso, ayo kutendeuka kupinda Kupisa simba mabasa.

mukana wokuti vanhu vanga ichi ane chimiro: d²s / dt² + 2β X DS / DT + ω²s = 0. In payakavakirwa ichi: s - ukoshi kwazvo muchikwidza nokuderedza inzwi kukosha iyo inechirevo ehupfumi imwe gadziriro, β - kugara unoratidza damping coefficient, ω - cyclic maitikiro.

Kushandisa nzira iyi inobvumira tinosvika kuna tsananguro oscillatory pezvakaitwa mu Linear enyika kubva chete nemaonero, uye zvakare kuti magadzirirwo uye simulation pamusoro oscillatory pezvakaitwa pamusoro zvesayenzi experimental chechetere.

Somuenzaniso, zvinozivikanwa kuti damped oscillations panguva yokupedzisira padariro kuonekwa kurega harmonic, kureva muchikwata kakawanda uye nguva yokuti vave kungoita maturo uye dzinofunga haana kuzivikanwa.

The klassiske nzira yokudzidza harmonic vibrations anoita harmonic oscillator. In nyore chimiro chiri hurongwa iyo rinorondedzera differential mukana wokuti vanhu vanga vane harmonic oscillations: DS / DT + ω²s = 0. Asi siyana oscillatory pezvakaitwa kunotungamirira muropa kuti pane vakawanda oscillators. Pano ndivo vanonyanya marudzi:

- Chitubu oscillator - chakaipa mutoro une rimwe guru m, iyo yakaturikwa pamusoro chitubu kwakavharwa nenyama. It oscillates harmonic mhando, izvo zvinorondedzerwa ne nzira F = - BR.

- panyama oscillator (zvakavamba kuchinja) - zvikukutu, oscillates dzakapoteredza kunofambira mberi akabatana pasi pokudzora imwe simba;

- kwemasvomhu zvakavamba kuchinja (mu mamiriro kushanda hariwanikwi). Zviri muenzaniso wakakwana hurongwa raiumbwa oscillating nomuviri une rimwe guru, iyo yakaturikwa pamusoro vanachandagwinyira hauremi shinda.