Kawm txog cov pendulum - yuav ua li cas nrhiav tau lub sij hawm ntawm ib tug yooj yim pendulum oscillation

Qhov ntau ntawm oscillatory dab uas koos peb, heev npaum li cas hais tias yog tsab - thiab muaj ib yam dab tsi uas tsis ywj faj ywj fwm? Tsis yog, vim txawm heev nyob khov kho kwv, hais ib lub pob zeb, uas yog ntau txhiab xyoo yog tseem, tseem oscillates dab - tsis tseg heats thaum lub sij hawm hnub, nce, thiab thaum hmo ntuj cools thiab shrinks. Thiab lub ze tshaj piv txwv - ntoo thiab tej ceg - xws li tas tag nrho nws lub neej. Tab sis, ces - lub pob zeb, ntoo. Thiab yog hais tias koj cia li poob siab yog hom twg los ntawm 100 zaj dabneeg tsev? Nws yog lub npe hu, piv txwv li, hais tias cov saum toj kawg nkaus Ostankinskaya ntauwd yog deflected mus mus los los ntawm 5-12 meters, zoo dua tsis muaj pendulum 500 m siab. Thiab kom deb li deb raws li nce nyob rau hauv loj zoo xws li cov siv los ntawm kub sib txawv? Ntawm no nws yog tau cais thiab kev co machine thiab mechanisms yees. Cia li xav hais tias, lub dav hlau nyob rau hauv uas koj ya tsis tu ncua mas nws txawv. Tsis txhob hloov koj lub siab ya? Nws yog tsis tsim nyog, vim hais tias cov hloov mus hloov los - yog lub essence ntawm lub ntiaj teb no nyob ib ncig ntawm peb, peb yuav tsis tau tshem ntawm lawv - lawv muaj peev xwm nkaus xwb yuav coj mus rau hauv tus account thiab thov cov "zoo rau".

Raws li ib txwm, txoj kev tshawb ntawm cov feem ntau complex chaw ntawm kev txawj ntse (thiab lawv cia li tsis tshwm sim) pib nrog ib tug kev taw qhia rau ib tug yooj yim qauv. Thiab muaj ib tug yooj yim thiab ntau to taub mus rau lub xaav qauv ntawm lub oscillatory txheej txheem, dua li cov pendulum. Nws yog ntawm no, nyob rau hauv txoj kev tshawb no ntawm physics, peb ua ntej hnov no mysterious kab lus - "sij hawm ntawm oscillation ntawm ib tug yooj yim pendulum." Pendulum - yog lub xov thiab load. Thiab yog dab tsi no xws li ib tug tshwj xeeb pendulum - Mathematics? Ib tug heev yooj yim, qhov no pendulum yog xav hais tias cov xov tsis muaj tus luj ntawm uas tsis yog-extensible, thiab cov ntaub ntawv uas taw tes vibrates nyob rau hauv tus ntawm lub ntiajteb txawj nqus. Qhov tseeb yog tias feem ntau, xav tias ib tug txheej txheem, piv txwv li, lub deeg tsis tau kiag li tag nrho cov account ntawm lub cev tus yam ntxwv xws li hnyav, elasticity, etc. Tag nrho cov neeg koom nyob rau hauv lub sim. Nyob rau tib lub sij hawm, tus ntawm ib co ntawm lawv nyob rau hauv tus txheej txheem yog negligible. Piv txwv li, ib tug priori nws yog to taub hais tias lub pendulum nyhav thiab elasticity xov nyob rau hauv tej yam tej yam kev mob tsis muaj hnov cov nyhuv rau lub sij hawm ntawm oscillation ntawm cov zauv pendulum yog negligibly me me, yog li lawv cawv yog cais los ntawm kev saib xyuas.

Kev txiav txim ntawm lub sij hawm ntawm oscillation ntawm lub pendulum, yog hais tias tsis yooj yim NW nyuam qhuav paub yog qhov no: lub sij hawm - lub lub sij hawm thaum lub sij hawm uas yuav siv sij hawm qhov chaw ib txhij oscillation. Wb ua ib lub cim nyob rau hauv ib tug ntawm cov huab cov ntsiab lus ntawm lub zog ntawm cov khoom. Tam sim no txhua txhua lub sij hawm ib tug taw tes yog kaw, ua suav tus xov tooj ntawm tiav oscillations thiab nco ntsoov lub sij hawm ntawm, hais tias, 100 deeg. Txiav txim seb lub caij ntawm ib lub sij hawm yog ib tug snap. Peb nqa tawm no xyaum ua tej yam rau oscillating nyob rau hauv ib tug dav hlau ntawm lub pendulum nyob rau hauv cov nram no mob:

- sib txawv thawj zaug amplitude;

- sib txawv load hnyav.

Peb yuav tau stunning tau tom ntej glance: nyob rau hauv txhua tus neeg mob, lub sij hawm ntawm ib tug yooj yim pendulum oscillation tseem unchanged. Nyob rau hauv lwm yam lus, cov amplitude thiab thawj zaug loj ntawm cov khoom taw tes rau lub caij ntawm lub sij hawm tsis pheev cawv. Rau ntxiv kev sib tham no tsuas yog ib downside - vim hais tias load qhov siab thaum tsav tsheb hloov, ces txoj kev txum tim quab yuam raws li txoj kev nce mus nce los, uas yog yooj yim rau suav. Me ntsis khib lav - laub pendulum kuj nyob rau hauv lub transverse kev taw qhia - nws pib piav qhia txog ib tug conical nto, lub sij hawm T ntawm kev sib hloov tseem tib yam, cov kev ceev ntawm lub zog nrog lub ib ncig V - qhov ncig, raws uas tsiv ib cargo S = 2πr, ib tug es ua quab yuam qhia raws voos kheej-kheej.

Tom qab ntawd peb xam lub sij hawm ntawm oscillation ntawm ib tug yooj yim pendulum:

T = S / V = 2πr / v

Yog hais tias qhov ntev ntawm lub xov l ho ntau cargo loj (tsawg kawg yog 15-20 lub sij hawm), thiab cov xov kaum sab xis ntawm inclination yog me me (me me amplitude), peb yuav xav hais tias cov es quab yuam P yog sib npaug zos rau cov centripetal quab yuam F:
P = F = m * V * V / r

Nyob rau lwm cov tes, lub sij hawm ntawm txoj kev txum tim quab yuam thiab caij ntawm inertia ntawm lub load yog sib npaug zos, thiab ces

P * l = r * (m * g), uas implies noj mus rau hauv tus account uas P = F, lub nram qab no kab zauv: r * m * g / l = m * v * v / r

Tsis yooj yim mus nrhiav tau tus tshaj tawm ntawm cov pendulum: v = r * √g / l.

Thiab tam sim no nco ntsoov tus thawj heev qhia rau lub sij hawm thiab tus tus nqi ntawm cov tshaj tawm:

T = 2πr / r * √g / l

Tom qab transformation mis lub sij hawm tseem ceeb zauv pendulum oscillation nyob rau hauv lub kawg daim ntawv no yog raws li nram no:

T = 2 π √ l / g

Tam sim no yav tas los experimentally tau kev tshwm sim ntawm lub ywj pheej ntawm cov oscillation lub sij hawm ntawm tus luj ntawm lub load thiab amplitude tau paub tseeb hais tias nyob rau hauv ib tug analytical daim ntawv thiab tsis zoo li mus yuav li ntawd "amazing", raws li lawv hais tias, raws li yuav tsum tau.

Ntawm lwm yam, kho tus tom kawg qhia rau lub sij hawm ntawm oscillation ntawm cov zauv pendulum, koj yuav saib tau ib lub sijhawm zoo los ntsuas cov acceleration ntawm lub ntiajteb txawj nqus. Nws yog txaus kom dhos rau ib tug siv pendulum tom tej taw tes ntawm lub ntiaj teb thiab mus ntsuas lub sij hawm ntawm nws oscillations. Thiab yog li ntawd, kuj poob nthav, ib tug yooj yim thiab straightforward pendulum tau muab peb ib tug zoo heev lub sij hawm mus kawm rau hauv lub tsev ntawm cov kev ceev ntawm lub ntiaj teb ua kiav txhab, mus txog mus nrhiav lub ntiaj teb mineral deposits. Tab sis hais tias yog ib zaj dabneeg.