Damped oscillation

Oscillatory dab puag ncig lub neeg qhov txhia chaw. Qhov no tshwm sim yog vim lub fact tias, firstly, nyob rau hauv cov xwm, muaj ntau ntau yam kev kawm (lub cev, cov tshuaj lom, organic, etc.), nyob rau hauv uas deeg tshwm sim, nrog rau cov damped oscillations. Secondly, nyob rau hauv cov kev muaj tiag nyob ib ncig ntawm peb muaj ib tug lossis loj ntau yam ntawm oscillating systems uas nws heev hav zoov yog txuas mus rau lub oscillatory dab. Cov dab yog tag nrho cov nyob ib ncig ntawm peb, lawv tuab lub khiav ntawm tam sim no nyob rau hauv lub nyob ntawm tej, lub teeb tshwm sim, yoj propagation, thiab tshaj. Nyob rau hauv lub kawg, tus txiv neej nws tus kheej, los yog es tib neeg lub cev, yog ib tug oscillating system, uas nws lub neej yog muab los ntawm ntau hom ntawm hloov mus hloov los - lub plawv dhia, kev ua pa, ntshav, povtseg zog.

Yog li ntawd, lawv yog kawm ntau yam sciences, xws li ua hauj lwm. Qhov yooj yim thiab thawj nyob rau hauv txoj kev tshawb no yog free deeg. Lawv tsiag ntawv los ntawm lub qaug ntawm lub vibrational zog ntawm tus mem tes, yog li lawv thaum kawg nres thiab vim hais tias xws hloov mus hloov los yog txiav txim los ntawm lub tswvyim ntawm damped oscillations.

Nyob rau hauv lub oscillatory tshuab objectively tshwm sim zog poob txheej txheem (nyob rau hauv cov neeg kho tshuab tshuab - vim hais tias ntawm tsis sib haum xeeb nyob rau hauv hluav taws xob - vim lub xub ntiag ntawm lub fais kuj). Uas yog vim li cas xws damped oscillations tsis tau dej num raws li harmonic. Muab no thawj zaug daim ntawv qhia, peb yuav nthuav qhia lej muab, piv txwv li, lub mechanics ntawm lub damped oscillations mis qhia raws li: F = - RV = -R dx / dt. Nyob rau hauv cov mis no, r kuj coefficient, ib qhov nqi. Raws li cov mis, peb yuav xaus hais tias tus nqi ntawm cov tshaj tawm (V) rau lub system nyob rau hauv kev faib ua feem rau cov kuj muaj nqis. Tab sis lub xub ntiag ntawm lub kos npe rau "-" txhais tau tias tus quab yuam vector (F) thiab ceev yog cov miv xwm.

Thov kab zauv thib ob Newton txoj cai lij choj, thiab kev noj mus rau hauv tus account tus ntawm kuj rog, kab zauv characterizes damped oscillation zog cov txheej txheem yuav siv sij hawm li nram qab no daim ntawv: nyob rau hauv lub xub ntiag ntawm lub kuj quab yuam muaj rau hauv daim: d ^ 2 x / dt2 + 2β dt / dt + ω2 x = 0. Nyob rau hauv cov mis no β - damping coefficient, uas qhia tus nqi ntawm no theem ntawm lub oscillatory txheej txheem.

Heev uas zoo sib xws equation yuav tau rau ib tug hluav taws xob Circuit Court, noj mus rau hauv tus account lub damping thiab ntxiv mus rau sab laug sab ntawm lub voltage nco thoob plaws lub resistor UR. Tsuas yog nyob rau hauv cov ntaub ntawv no, lub differential kab zauv yog tsis sau rau lub sij hawm offset (t), thiab them lub capacitor q (t); kev sib txhuam coefficient r yog hloov los ntawm cov hluav taws xob Circuit Court kuj R; 2 nyob rau β = R / L, qhov twg K - Circuit Court kuj, L - ntev ntawm lub saw.

Yog hais tias nyob rau hauv lub hauv paus ntawm cov qauv no mus txua lub sib nug xov los, koj yuav pom tias lub teeb ntawm damped oscillations yog heev uas zoo sib xws graphics harmonic oscillations, tab sis lub amplitude ntawm lub oscillations maj txo exponentially.

Muab qhov tseeb hais tias oscillations yuav ua tau los ntawm ntau yam oscillatory systems thiab tshwm sim nyob rau hauv ib tug ntau yam ntawm tej kev kawm, nws yog tsim nyog los stipulate hais tias, zoo li cas ntawm system peb xav txog nyob rau hauv txhua rooj plaub. Los ntawm tus mob no nyob ntawm seb tsis tsuas yog nyob rau nta tshwj xeeb ntawm lub oscillatory dab, tab sis muaj yog qhov opposite nyhuv - qhov ntawm oscillations yog txiav txim los ntawm lub system nws tus kheej thiab nws cov kev faib qhov chaw. Peb tau, nyob rau hauv cov ntaub ntawv no, pom tias yog ib nyob rau hauv uas lub zog ntawm cov system nyob twj ywm unchanged thaum lub sij hawm ntawm txoj kev tshawb oscillatory txheej txheem. Piv txwv li, peb xav hais tias tus txheej txheem tsis hloov lub elasticity ntawm lub caij nplooj ntoos hlav, tus quab yuam ntawm lub ntiajteb txawj nqus yeeb yam nyob rau hauv cov load, thiab hluav taws xob nyob li qub nyob rau cov kuj ntawm cov kev ceev los yog acceleration ntawm lub oscillating qhov tseem ceeb. Tej oscillatory systems raug xa mus rau raws li linear.