Kab zauv harmonic oscillations thiab nws tseem ceeb nyob rau hauv txoj kev tshawb no ntawm qhov xwm ntawm oscillatory dab

Tag nrho cov harmonics muaj ib tug zauv qhia. Lawv lub zog characterizes lub teeb ntawm trigonometrical sib npaug, lub complexity ntawm uas yog txiav txim los ntawm lub complexity ntawm lub oscillatory txheej txheem, system zog thiab cov ib puag ncig nyob rau hauv uas lawv tshwm sim, i.e., rau lwm yam rau cov oscillation txheej txheem.

Piv txwv li, nyob rau hauv lub mechanics ntawm harmonic oscillation yog ib tug zog, uas yog yus muaj los ntawm:

- straightforward cim;

- sis tsis ncaj;

- tsiv cev nqaij daim tawv, uas tshwm sim los ntawm ib tug sine los yog cosine trajectory raws li ib tug muaj nuj nqi ntawm lub sij hawm.

Raws li cov kev zog, yuav ua rau harmonic oscillations kab zauv, uas muaj rau hauv daim:

x = ib tug cos ωt los yog daim ntawv x = ib tug txoj kev txhaum ωt, qhov twg x - tswj tus nqi A - tus nqi ntawm cov amplitude ntawm oscillation, ω - coefficient.

Xws li ib tug kab zauv ntawm harmonic oscillations yog qhov tseem ceeb rau tag nrho cov harmonic oscillations, uas yuav sib tham txog nyob rau hauv lub kinematics thiab mechanics.

Qhov taw qhia ωt, uas nyob rau hauv cov mis no sawv rau lub kos npe rau ntawm lub trigonometric functions, hu ua theem thiab nws qhia qhov chaw ntawm lub oscillating loj taw tes rau ib lub sij hawm ntawm ib tug muab amplitude. Thaum xaiv cov cyclic hloov mus hloov los active tivthaiv yog 2n, nws qhia tau hais tias cov xov tooj ntawm cov neeg kho tshuab deeg tsis pub dhau lub sij hawm mus los thiab yog denoted w. Nyob rau hauv cov ntaub ntawv no, lub kab zauv ntawm harmonic oscillations muaj nws raws li ib tug Performance index nqi ntawm ib tug cyclic (yeej) zaus.

Peb xaiv cov kab zauv ntawm harmonic oscillations, raws li twb tau sau tseg, yuav siv sij hawm ntau hom, nyob ntawm seb ob peb yam tseem ceeb. Piv txwv li, ntawm no yog ib qho kev xaiv. Yuav tau xav txog lub differential kab zauv ntawm free harmonic oscillations, ib tug yuav tsum xav txog qhov tseeb hais tias lawv tag nrho cov yuav attenuation. Cov ntau hom ntawm oscillation, qhov no tshwm sim manifests nws tus kheej nyob rau hauv ntau txoj kev: nres ib tug mus lub cev, lub tawg txiav nyob rau hauv hluav taws xob. Ib tug piv txwv yooj yim illustrating yuav txo tau ntawm oscillatory tej zaum, nws hloov dua siab tshiab rau hauv tshav kub zog ua.

Qhov no kab zauv muaj rau hauv daim: d²s / dt² + 2β x ds / dt + ω²s = 0. Nyob rau hauv cov mis no: s - tus nqi fluctuating nqi uas characterizes lub thaj chaw ntawm ib tug system, β - qhov uas qhia ib damping coefficient, ω - cyclic zaus.

Siv cov mis tso cai rau lub mus kom ze rau qhov kev piav qhia ntawm oscillatory dab nyob rau hauv linear tshuab los ntawm ib tug tib seem yus pom, thiab kuj yuav ua rau tus tsim thiab simulation ntawm oscillatory dab rau scientific sim theem.

Piv txwv li, nws yog lub npe hu hais tias damped oscillations nyob rau theem kawg ntawm nws ces cease yuav harmonic, piv txwv li lub qeb ntawm qhov zaus thiab sij hawm rau lawv los ua tsuas meaningless thiab neeg pab leg ntaubntawv yog tsis yog tsis paub.

Lub classic txoj kev kawm harmonic deeg ua harmonic oscillator. Nyob rau hauv lub nyuaj daim ntawv nws yog ib tug system uas qhia txog ib tug txawv kab zauv ntawm harmonic oscillations: ds / dt + ω²s = 0. Tab sis manifold oscillatory dab ua ib txwm rau lub fact tias muaj yog ib tug loj tus naj npawb ntawm oscillators. Ntawm no lawv muaj lub ntsiab hom:

- ib tug caij nplooj ntoos hlav oscillator - qub load muaj ib tug tej yam loj m, uas yog tshem tawm rau ib tug elastic caij nplooj ntoos hlav. Nws oscillates harmonic yam, uas yog piav los ntawm cov mis F = - kx.

- lub cev oscillator (pendulum) - khoom, oscillates nyob ib ncig ntawm ib tug zoo li qub axis nyob rau hauv tus ntawm ib tug tej yam quab yuam;

- zauv pendulum (nyob rau hauv qhov suab tsis tshwm sim). Nws yog ib qho zoo tagnrho qauv system muaj lub oscillating lub cev lub cev muaj ib tug tej yam loj, uas yog tshem tawm rau ib tug nruj heev weightless threads.