Zvakavamba kuchinja: nguva uye kumhanyisa kuti fomura

The zvokuimba maitiro kuti rine zvinhu pfungwa (muviri), iyo yakaturikwa munhu hauremi inextensible filament (ayo gobvu ndiro kunyora nezvavo zvichienzaniswa uremu muviri) ari yunifomu rinokweva munda, akadana kwemasvomhu zvakavamba kuchinja (rimwe zita - the oscillator). Kune mamwe marudzi namano. Panzvimbo imwe filament hauremi tsvimbo anogona kushandiswa. Zvakavamba kuchinja anogona zvakajeka zvinoratidza musimboti dzakawanda dzinonakidza mananara. Kana diki amplitude vibrations waro inofamba anonzi harmonic.

General ruzivo pamusoro zvokuimba hurongwa

The yemaitiro pamusoro oscillation nguva zvakavamba kuchinja yakanga akatunhidzwa Dutch musayendisiti Huygens (1629-1695 gg.). Izvi akararama Isaac Newton akanga kwazvo kwazvo pakati zvokuimba hurongwa. Muna 1656 iye akasika makarinda wokutanga une zvakavamba kuchinja mashandiro. Ivo akayera nguva yokunyanyisa nemazvo nguva idzodzo. kuvamba ichi raiva danho guru kukura mumuviri kuedza uye inoshanda mabasa.

Kana zvakavamba kuchinja zviri imwe zvakanyatsoenzana nzvimbo (akarembera vertically), kuti simba regiravhiti achapiwa zvinodzikamiswa mavara makakatanwa simba. Flat zvakavamba kuchinja pamusoro asiri stretchable pemavara ndiyo hurongwa pamwe madhigirii maviri rusununguko yokukurukurirana. Kana kuchinja chete chezvinonhuwira kuchinja hunhu zvose nhengo dzayo. Somuenzaniso, kana munhu neshinda kuchatsiviwa tsvimbo, ipapo ichi zvokuimba kwava chete 1 mwero rusununguko. Ko, zvino, zvivako munhu akarongeka zvakavamba kuchinja? In ichi nyore ezvinhu, pasi pokudzora kwenguva nenguva perturbation, mhirizhonga anooneka. Kana zvakadaro kana kuturika pfungwa hakusi, uye oscillates munhu zvakavamba kuchinja, pane itsva zvakanyatsoenzana chinzvimbo. Kana nokukurumidza nokufamba uye pasi ichi zvokuimba maitiro anova akatsiga nzvimbo "zvachose pasi." Rinewo zita rayo. Inonzi Kapitza zvakavamba kuchinja.

The ehupfumi pakati zvakavamba kuchinja

Zvakavamba kuchinja ane ehupfumi zvinonakidza chaizvo. Vose dzinotsigirwa nemitemo inodzora kuzivikanwa. Nguva oscillation pakati zvakavamba kuchinja zvimwe anoenderana ezvinhu akasiyana-siyana akadai saizi uye chimiro womuviri, daro pakati pfungwa kuturika uye muzinda regiravhiti, kuparadzirwa uremu panyaya iyi. Ndokusaka tsanangudzo muviri yakarembera nguva iwayo akaoma. Zviri nyore kuverenga nguva nyore zvakavamba kuchinja, asi nzira iyo anopiwa pazasi. Somugumisiro vachichengeta mapatani izvi zvinogona kuisa zvakafanana zvemaziso gadziriro:

• Kana, apo kuramba chete pakureba zvakavamba kuchinja, ambomiswa zvakasiyana siyana mitoro, nguva oscillation kuwana chete, kunyange zvazvo kwavo uremu achizosiyana zvikuru. Somugumisiro, nguva zvakavamba kuchinja hakunei kurema mutoro.

• Kana hurongwa anotanga kuramba ari zvakavamba kuchinja hakusi yakakurisa, asi zvakasiyana pamakona, zvichaita-chinja pamwe chete nguva, asi panguva amplitudes zvakasiyana. Nepo zvarakasiya kubva pakati nepakati haisi wakakurisa nokufamba kwavo chimiro achava pedyo zvakakwana harmonic. Nguva imwe zvakavamba kuchinja kwakadaro hakubvi pane vibrational amplitude. pfuma iyi zvokuimba gadziriro inonzi isochronism (muchiGiriki "chronos" - nguva "Izosov" - vakaenzana).

Nguva imwe nyore zvakavamba kuchinja

Nhamba iyi inomiririra kwomuzvarirwo nguva oscillation. Pasinei kunzwisisa idzidziso, muitiro pachayo nyore chaizvo. Kana urefu rwebhuruu kwemasvomhu zvakavamba kuchinja L, uye rinokweva kumhanyisa g, ukoshi ichi akaenzana:

T = 2π√L / d

Small nguva dzinongoitika oscillations hakuna nzira hakubvi pane vakawanda zvakavamba kuchinja uye oscillation amplitude. Muchiitiko chino, somunhu kwemasvomhu zvakavamba kuchinja kunoita pamwe kuderedzwa kureba.

Oscillations ane kwemasvomhu zvakavamba kuchinja

Kwemasvomhu zvakavamba kuchinja oscillates, iyo inogona kurondedzerwa kunoitwa nyore differential mukana wokuti vanhu vanga:

X + ω2 chivi x = 0,

apo X (T) - vasingazivikanwi nerevane (angled iyi Kutsauka apasi chinzvimbo zvakanyatsoenzana panguva t, chinoratidzwa radians); ω - yakanaka kugara zvakatemwa kubva parameters pakati zvakavamba kuchinja (ω = √g / L, apo d - the kumhanyisa regiravhiti, uye L - kureba nyore zvakavamba kuchinja (kuturika).

Mukana wokuti vanhu vanga maduku oscillations pedyo zvakanyatsoenzana nzvimbo (harmonic mukana wokuti vanhu vanga) sezvinotevera:

X + ω2 chivi x = 0

Oscillatory inofamba pakati zvakavamba kuchinja

Zvakavamba kuchinja, izvo zvinoita oscillations diki, kutamira sinusoid. Second murayiro differential mukana wokuti vanhu vanga rinoungana zvose zvinodiwa uye parameters ane kufamba kwakadaro. Kuziva nzira unofanira kuisa nokukurumidza uye Coordonatele, gare gare vakatsunga yakazvimirira constants:

x = A chivi (θ ₀ + ωt),

apo θ ₀ - Paunotanga, A - amplitude pamusoro oscillation, ω - cyclic maitikiro kwakatemwa kubva equations inofamba.

Zvakavamba kuchinja (fomura nokuti makuru amplitudes)

, Ichi zvokuimba maitiro kuita oscillations yavo hombe amplitude, zviri pasi mitemo yakawanda kunzwisisa motokari. vari dzaona maererano nzira kuti zvakavamba kuchinja kwakadaro:

chivi X / 2 = nepfambi * Ose sn (ωt / u),

apo Ose sn - Sine Jacobi, uyo a <1 kwenguva nenguva basa, uye nokuda nepfambi diki izvozvo rinobatana mano trigonometric Sine. Kukosha nepfambi kunotemwa nemashoko anotevera okuti:

U = (ε + ω2) / 2ω2,

apo ε = E / mL2 (mL2 - simba zvakavamba kuchinja).

Kutsunga nonlinear oscillation nguva zvakavamba kuchinja nokuda mutoo:

T = 2π / Ω,

apo Ω = π / 2 * ω / 2K (u), K - rakaita denderedzwa chairo chinokosha, π - 3,14.

zvakavamba kuchinja kwebasa separatrix

It rinonzi separatrix trajectory pamusoro guru ino, umo maviri-dimensional kutotanga nzvimbo. Zvakavamba kuchinja zvinofamba asiri nguva nenguva. In pfungwa zvikuru kure kwenguva anosiya kubva zvakanyanyisa repamusoro nzvimbo kune razero nokukurumidza, uye zvino ari zvishoma nezvishoma tiwane. Iye pakupedzisira akamira, achidzokera nzvimbo yaro yepakutanga.

Kana amplitude pakati oscillation pakati zvakavamba kuchinja anosvika nhamba Pi, zvinonzi kuti inofamba iri Pasika mundege riri pedyo kuti separatrix. Panyaya iyi, pasi zvinoitwa duku nguva nenguva dzokutyaira rehondo zvokuimba hurongwa rinoratidza runobva maitiro.

Panguva chiitiko kungoti zvakavamba kuchinja kubva zvakanyatsoenzana nzvimbo pamwe necheparutivi CP kunoitika tangential simba Fτ = -mg chivi φ negiravhiti. "Kubvisa" chiratidzo zvinoreva kuti tangential zvinoriumba rinotungamirirwa mu negwara kubva nechokugedhi kutsauka pane zvakavamba kuchinja. Kana achireva Via zvakavamba kuchinja misha X pamwe munhu raundi chinhu chakakombama ine nharaunda L akaenzana ayo chisina kutsetseka misha φ = X / L. Mutemo wechipiri Isaaka Nyutona, yakagadzirirwa fungidziro pamusoro kumhanyisa Vector uye simba akapa achida ukoshi:

MG τ = Fτ = -mg chivi X / L

Kubva musi reshiyo ichi, zviri pachena kuti zvakavamba kuchinja chinhu nonlinear ezvinhu, sezvo simba kuti uderedze kudzokera ayo zvakanyatsoenzana chinzvimbo, haasi nguva dzose Proportional kune misha X, chivi X / L.

Chete kana kwemasvomhu zvakavamba kuchinja anoita vibrations diki, ndiko harmonic oscillator. Mune mamwe manzwi, inova zvokuimba gadziriro anokwanisa kuita harmonic oscillations. rakada ichi chinoshanda kwerinenge pamakona 15-20 °. Zvakavamba kuchinja makuru amplitudes hakusi zvinopindirana.

mutemo Newton nokuda oscillations chiduku zvakavamba kuchinja

Kana zvokuimba hurongwa anoita oscillations diki, mutemo 2nd Newton kuchaita seizvi:

MG τ = Fτ = -m * g / L * x.

On hwaro ichi, tinogona kugumisa kuti tangential kumhanyisa kungoti zvakavamba kuchinja zviri Proportional kuti misha dzaro chiratidzo "kubvisa". Ichi chirwere yokuti hurongwa inova harmonic oscillator. Module proportionality chinokonzera pakati misha uye kumhanyisa vakaenzana muchivara ari chisina kutsetseka maitikiro:

ω02 = g / L; ω0 = √ g / L.

mutoo uyu unoratidza kwomuzvarirwo kakawanda oscillations duku kwaiita zvakavamba kuchinja. On hwaro ichi,

T = 2π / ω0 = 2π√ g / L.

Masvomhu inobva mutemo kuchengetedza simba

Properties oscillating zvakavamba kuchinja masangano inogona kurondedzerwa tichibatsirwa mutemo kuchengetedza simba. Zvinofanira kurangarirwa kuti zvinogona nesimba zvakavamba kuchinja mune rinokweva Munda:

E = mgΔh = mgL (1 - Kosi α) = mgL2sin2 α / 2

Full zvokuimba simba vakaenzana ari kinetic uye kunonyanyisa zvinogona: Epmax = Ekmsx = E

Kana zvakanyorwa mumutemo kuchengetedza simba, Achibata rinobva ari kurudyi mativi mukana wokuti vanhu vanga:

Ep + Ek = const

Sezvo rinobva pakati constants akaenzana 0, ipapo (Ep + Ek) '= 0. The rinobva pakati Verengai vakaenzana Verengai nomukaka:

Ep '= (MG / L * x2 / 2)' = MG / 2L * 2x * x '= MG / L * V + Ek' = (mv2 / 2) = m / 2 (v2) '= m / 2 * 2v * V '= mv * α,

Naizvozvo:

MG / L * XV + mva = V (MG / L * X + M α) = 0.

Zvichienderana rokupedzisira payakavakirwa, tinowana: α = - g / L * x.

Practical pokushandisa kwemasvomhu zvakavamba kuchinja

Kumhanyisa rusununguko kuwa kunosiyana-siyana pamwe Latitude, nokuti arambe achirema pamusoro goko vakapoteredza nyika haina kufanana. Apo matombo kuitika ane yepamusoro arambe achirema zvichava zvishoma kwirirei. Kumhanyisa pamusoro kwemasvomhu zvakavamba kuchinja rinowanzoshandiswa kudziongorora. In yayo rubatsiro tsvakai zvicherwa zvakasiyana. Simply Anoverenga oscillations ane zvakavamba kuchinja, zvinokwanisika kuona marasha kana mhangura norudo Pasi. Izvi imhaka yokuti zvinhu izvi vane arambe achirema uye kurema kupfuura nhema pasi anodzora matombo.

Kwemasvomhu zvakavamba kuchinja akashandiswa vakakurumbira nyanzvi saSocrates, Aristotle, Plato, Plutarch, Archimedes akadaro. Vazhinji vavo vaidavira kuti zvokuimba hurongwa vatingakurudzira njodzi uye upenyu. Archimedes akashandisa kwemasvomhu zvakavamba kuchinja pamwe Masvomhu ake. Mazuvano, occultists zhinji uye vafemberi vanoshandisa ichi zvokuimba maitiro nokuda Implementation uprofita ayo, kana kutsvaka zvisipo vanhu.

The akakurumbira muongorori wenyeredzi wokuFrance uye musayendisiti, Flammarion kwavo kuongorora akashandisa kwemasvomhu zvakavamba kuchinja. Aiti kuti nokubatsirwa ake akakwanisa kufungidzira kuwanikwa pasi idzva, kuti chidzoke of Tunguska meteorite, uye zvimwe zviitiko zvinokosha. Panguva Second World War mu Germany (Berlin) aishanda ari kushandiswa Institute zvakavamba kuchinja. Mazuvano, kutsvakurudza kwakadaro hakusi iripo Munich Institute of Parapsychology. basa rake zvakavamba kuchinja tsvimbo sangano iri rinonzi "radiesteziey".