Mitu pa harmonic oscillation, nthawi, nthawi, physics giredi 12

Funso 1.Mukuwona: 12 Physical Time Axis

Chinthu chimayenda molumikizana ndi nthawi ya T. Sankhani nthawi yoyambira (t = 0) kuti ikhale nthawi yomwe chinthucho chikuwoloka malo ogwirizana, chinthucho chimakhala pamalire kwa nthawi yoyamba panthawiyo.

. $\dfrac{T}{4}$.

Mukuwona: 12 Physical Time Axis

. $\dfrac{T}{2}$.. $\dfrac{T}{6}$.. $\dfrac{T}{8}$.

Malingana ndi nthawi yogawa nthawi, nthawi yopeza ndi t = $\dfrac{T}{4}$.

Ndime 2.

Chinthu chimayenda mozungulira ndi nthawi T. Nthawi yaifupi kwambiri yomwe imatenga kuti chinthu chisunthe kuchokera kumalire ena kupita kumalo ena.

. $\dfrac{T}{4}.$. $\dfrac{T}{6}.$. $\dfrac{T}{8}.$. $\dfrac{T}{2}.$

Ndime 3.

Chinthu chimayenda molumikizana ndi nthawi T, matalikidwe A. Nthawi yoyambira imasankhidwa ngati nthawi yomwe chinthucho chikudutsa malo ofananirako, chinthucho chili pa malo a 0.5A kutali ndi malo ogwirizana kwa nthawi yoyamba.

. $\dfrac{T}{12}$.. $\dfrac{T}{4}$.. $\dfrac{T}{6}$.. $\dfrac{T}{2}$.

Malingana ndi nthawi yogawa nthawi, nthawi yopeza ndi t = $\dfrac{T}{12}$

Ndime 4.

Chinthu chimayenda ndi nthawi T. Chiyambi cha nthawi chimasankhidwa ngati nthawi yomwe chinthucho chili pamalire, chinthucho chili ndi 0.5A kutali ndi malo oyenerera kwa nthawi yoyamba panthawiyo.

. $\dfrac{T}{6}$.. $\dfrac{T}{8}$.. $\dfrac{T}{4}$.. $\dfrac{T}{2}$.

Malinga ndi kagawidwe ka nthawi, nthawi yopeza ndi t = $\dfrac{T}{6}$

Funso 5.

An chinthu oscillates mu harmonic zoyenda ndi nthawi T, matalikidwe A. Sankhani nthawi chiyambi pamene chinthu pa malo osachepera kusamutsidwa, chinthu ali pa udindo wa 0,5A kusamutsidwa kwa nthawi yoyamba pa nthawi.

. $\dfrac{T}{3}$.. $\dfrac{T}{6}$.. $\dfrac{T}{2}$.. $\dfrac{T}{4}$.

Ndime 6.

Tinthu tating’onoting’ono timazungulira molumikizana ndi ox ox ndi equation \(cm, s). Kuwerengedwa kuyambira nthawi yomwe \ tinthu tating’onoting’ono timadutsa pamalo a mtunda woyipa \ koyamba pa nthawi:

. 0.50s ku.. 0.23s ku.. 0.77s ku.. 0.60s ku.

Pa t = 0, φ = $-\dfrac{\pi}{3}$ → \. Tili ndi ma oscillation pamagawo ogawa nthawi:

Choncho nthawi yoti mupeze ndi: t = $\dfrac{T}{6}+\dfrac{T}{4}+\dfrac{T}{6}=\dfrac{7T}{12}=0.23\ text{ s}$.

Ndime 7.

Thupi laling’ono limayenda moyenda molumikizana ndi matalikidwe a 8 cm, ma frequency aang’ono $\dfrac{2\pi}{3}$(rad/s) , pa nthawi yoyambirira t = 0 chinthucho chimadutsa pamtunda $4 \sqrt{ 3}$ masentimita kumbali yabwino. Nthawi yoyamba kuyambira t = 0 chinthucho chili ndi mtunda wocheperako

. 1.75s ku. 0.75s ku. 1.25 mz.. 0.5s ku

Ndime 8.

Thupi laling’ono limazungulira molingana ndi matalikidwe a 10 cm, pafupipafupi 0,5 Hz, pa nthawi yoyamba t = 0 chinthucho chimadutsa pamalo omwe ali ndi mtunda wa -5 cm munjira yabwino. Nthawi yoyamba chinthucho chikudutsa malo a mtunda $-5\sqrt{2}$cm kumbali yabwino popeza t = 0 ndi

. $\dfrac{13}{6}$s.. $\dfrac{21}{12}$s. $\dfrac{13}{12}$s. $\dfrac{23}{12}$s

Choncho nthawi yoti mupeze ndi: t = $\dfrac{T}{3}+\dfrac{T}{2}+\dfrac{T}{8}=\dfrac{23T}{24}=\dfrac{23 {12}\mawu{s}$.

Ndime 9.

Chinthucho chimagwedezeka molingana ndi equation: x = 4cos(8πt – π/6)cm. Nthawi yaifupi kwambiri yoti chinthu chichoke pa \cm kunjira yabwino kupita pamalowo ndi mtunda \cm munjira yabwino ndi:

. $\dfrac{1}{10}$(s). $\dfrac{1}{16}$(s).. $\dfrac{1}{20}$(s). $\dfrac{1}{12}$(s).

Nthawi yaifupi kwambiri yomwe mungapeze ndi: ∆t = $\dfrac{T}{6}+\dfrac{T}{6}=\dfrac{T}{3}=\dfrac{1}{12}\text { s}$.

Ndime 10.

Chinthu chimagwedezeka ndi nthawi T = 2 s. Nthawi yaifupi kwambiri yoti chinthu chichoke pa mfundo M yokhala ndi mtunda x = 0.5A kupita kumalire abwino ndi

. $\dfrac{1}{3}$(s).. $\dfrac{1}{6}$(s).. $\dfrac{1}{12}$(s). 0.25 (s

Kanthawi kochepa kwambiri komwe mungapeze ndi: $\Delta t=\dfrac{T}{6}=\dfrac{2}{6}\text{= }\dfrac{1}{3}\text{s}$

Ndime 11.

Chinthucho chikuzungulira, lolani $t_{1}$ ikhale nthawi yaifupi kwambiri yomwe imatengera chinthucho kuchoka ku VTCB kupita ku li x = 0.5A ndipo $t_{2}$ ndiyo nthawi yaifupi kwambiri yomwe imatenga chinthucho kuchoka pa malo li x. = 0.5A mpaka li. Dongosolo lolondola ndi

. $t_{1}$ = 2$t_{2}$. $t_{1}$ = 4$t_{2}$. $t_{1}$ = $t_{2}$. $t_{1}$ = 0.5$t_{2}$

Ndime 12.

Kasupe wa pendulum amazungulira ndi matalikidwe A, nthawi yaifupi kwambiri yomwe cholembera chimatengera kuti cholembera chichoke pamalo atali ${{x}_{1}}=-\dfrac{A\sqrt{2}}{2}$ mkati njira yabwino yopita kumalo komwe mtunda wa ${{x}_{1}}=-\dfrac{A}{2}$ kumbali yolakwika ndi 1.7 s. Nthawi ya oscillation ya pendulum ndi

. 6 s. 2.4s ku. 3 s. 2.55s ku

Nthawi yayifupi kwambiri ndi: t = $\dfrac{T}{8}+\dfrac{T}{4}+\dfrac{T}{3}=1.7\text{s }\to \mawu {T = 2.4 s}$.

Ndime 13.

Kasupe wa pendulum amazungulira ndi matalikidwe A. Nthawi yaifupi kwambiri yomwe imatenga kuti chinthu chiyende kuchokera pamalo ofananira kufika pamalopo M ndi mtunda $\dfrac{A\sqrt{2}}{2}$ ndi 0.25(s) ). Nthawi ya pendulum

. 2s. 1 mphindi. 0.5s. 1.5s

Ndime 14.

Pendulum ya kasupe imapindika ndi matalikidwe A, nthawi yaifupi kwambiri yomwe imatenga kuti cholembera chichoke pamalo amtunda $x_{1}$ = – A kufika pamalo a digiri $x_{2}$ = 0 ,5A ndi 1 s . Nthawi ya oscillation ya pendulum ndi

. 2 s. 6s .. 1/3 ms. 3 s

Ndime 15.

Chinthu chimagwedezeka ndi matalikidwe A ndi mafupipafupi 5 Hz. Nthawi yayifupi kwambiri yoti chinthu chichoke pamalo a mtunda $x_{1}$ = – 0.5A kupita pamalo a mtunda $x_{2}$ = 0.5A ndi

. $\dfrac{1}{10}$s. $\dfrac{1}{20}$s. $\dfrac{1}{30}$s.. 1 mphindi

Ndime 16.

Chinthu chimayenda molumikizana ndi nthawi ya T. Nthawi yaifupi kwambiri yomwe imatenga kuti chinthu chisunthe kuchokera pamalo ofananira kupita kunjira yabwino kupita pamalo osasunthika pang’ono.

. $\dfrac{T}{2}$. $\dfrac{2T}{3}$.. $\dfrac{T}{8}$.. $\dfrac{3T}{4}$.

Malo ochepera li ndi malo ofanana ndi x = – A.

$\Delta t=\Delta {{t}_{1}}+\Delta {{t}_{2}}=\dfrac{T}{4}+\dfrac{T}{2}=\dfrac{ 3T}{4}$

Ndime 17.

Chinthu chimazungulira mozungulira ndi nthawi T, matalikidwe A. Nthawi yaifupi kwambiri pakati pa nthawi ziwiri zotsatizana chinthucho ndi 0.5A kuchokera pa malo ofanana ndi

Nthawi yodutsa pakati pa zinthu ziwiri zotsatizana 0.5A kuchokera ku VTCB ikhoza kukhala $\Delta {{t}_{1}}=\dfrac{T}{6}$ kapena $\Delta {{t}_{2 }}=\ dfrac{T}{3}$, kotero kuti nthawi yayifupi kwambiri yopeza ndi $\dfrac{T}{6}$.

Ndime 18.

Chinthu chimazungulira moyenda molumikizana ndi nthawi T, matalikidwe A. Kanthawi kochepa kwambiri pakati pa nthawi ziwiri zotsatizana za mtunda $\dfrac{A}{2}$ ndi

. $\dfrac{T}{6}$.. $\dfrac{T}{4}$.. $\dfrac{T}{3}$.. $\dfrac{T}{2}$.

Nthawi yapakati pa zinthu ziwiri zotsatizana za 0.5A ikhoza kukhala $\Delta{{t}_{1}}=\dfrac{T}{3}$ kapena $\Delta {{t}_{2}}=\dfrac{2T }{3}$, kotero kuti nthawi yaifupi kwambiri yopeza ndi $\dfrac{T}{3}$.

Ndime 19.

Chinthu chimazungulira moyenda molumikizana ndi nthawi T, matalikidwe A. Nthawi yaifupi kwambiri pakati pa nthawi ziwiri zotsatizana chinthucho chili kutali ndi malo ofananira $\dfrac{A\sqrt{3}}{2}$ ndi

. $\dfrac{T}{8}$.. $\dfrac{T}{4}$.. $\dfrac{T}{2}$.. $\dfrac{T}{6}$.

Nthawi yaifupi kwambiri pakati pa zinthu ziwiri zotsatizana zikuyenda kuchokera pamalo ofanana $\dfrac{A\sqrt{3}}{2}$ ndi : $\Delta t=2.\dfrac{T}{12}=\dfrac{T {6}$

Ndime 20.

Chinthu chimayenda moyenda molumikizana ndi matalikidwe A. Pambuyo pa nthawi yaifupi kwambiri ya 0.05 s, kulemera kwa pendulum kumabwereranso mtunda womwewo d (d) kuchokera pa malo ofanana. . 5 Hz pa. 2 Hz pa. 10hz pa

$\Delta {{t}_{1}}=\dfrac{T}{4}$ iliyonse imapezanso mtunda kuchokera ku VTCB d1 = $\dfrac{A\sqrt{2}}{2}$

Zosavuta kuwona, $\Delta iliyonse {{t}_{2}}=\dfrac{T}{2}$ chinthucho chili pamalire awiri, mwachitsanzo d2 = A kuchokera ku VTCB.

Chifukwa chake Δt1 = 0.5Δt2.

Ndime 22.

Tinthu tating’onoting’ono tomwe timazungulira tinthu tating’onoting’ono ta 10 cm. Nthawi yaifupi kwambiri yoti chinthu chiziyenda kuchokera pamalo -2.5 cm munjira yolakwika mpaka kufika pakusamuka kwakukulu ndi 2.5 s. Chiwerengero cha oscillation okwana opangidwa ndi thupi 2 mphindi ndi

. 32. 30. 20. 50

Amplitude A = 5 cm.

Zosavuta kuwona: $\Delta t$ = $\dfrac{T}{6}+\dfrac{T}{2}$ = 2.5 s → T = 3.75 s.

Kotero mphindi 2 = 120 s, chiwerengero chonse cha oscillation chopangidwa ndi thupi ndi $\dfrac{120}{3.75}=32$ .

Ndime 23.

Chinthu chimayenda molumikizana ndi ox ox, malo ofananirako pa O ndi pafupipafupi f = 2 Hz, chodziwika poyambira chinthu chomwe chimagwirizanitsa x = – 3 cm chikuyenda molakwika ndiyeno nthawi yayifupi kwambiri $\ dfrac{1}{6}$s, chinthucho chidzabwerera ku zogwirizanitsa zoyambirira. The equation wa kayendedwe ka thupi ndi

. $x=3\sqrt{3}\cos \left( 8\pi t-\dfrac{\pi}{6} \kumanja)\left(cm \right)$.. $x=6\cos \kumanzere( 4\pi t+\dfrac{\pi}{3} \kumanja)\kumanzere(cm \kumanja)$. $x=6\cos \left( 4\pi t-\dfrac{\pi}{3} \kumanja)\left(cm \right)$. $x=6\cos \left( 4\pi t+\dfrac{2\pi}{3} \kumanja)\left(cm \right)$

Mofanana ndi chitsanzo mu nkhani kanema

Tili ndi T = $\dfrac{1}{2}$ s → $\Delta t=\dfrac{1}{6}s=\dfrac{T}{3}$. Choncho, molingana ndi kagawidwe ka nthawi x = -3 cm = $-\dfrac{A}{2}\to A=6\text{ }cm$

Poyambirira, t = 0, chinthucho chili ndi x = $-\dfrac{A}{2}$ (-) → gawo loyambirira φ = $\dfrac{2\pi }{3}$ .

Ndime 24.

Chinthu chozungulira pa axis Ox, malo ofanana pa O amapanga 100 oscillation wathunthu mu 50 s. Nthawi yoyamba chinthu chogwirizanitsa x = – 4 masentimita chikuyenda bwino ndipo nthawi yaifupi kwambiri ndi 0.375 s, chinthucho chimabwerera ku mgwirizano wapachiyambi. The equation wa kayendedwe ka thupi ndi

. $x=8\cos \left( 4\pi t+\dfrac{2\pi}{3} \kumanja)\kumanzere(cm \kumanja)$. $x=8\cos \left( 4\pi t-\dfrac{2\pi}{3} \kumanja)\left(cm \right)$. $x=4\sqrt{2}\cos \left( 8\pi t+\dfrac{3\pi}{4} \kumanja)\left(cm \right)$.. $x=4\sqrt{2}\cos \left( 4\pi t-\dfrac{3\pi}{4} \kumanja)\kumanzere(cm \kumanja)$

T = 0.5(s) → ω = 4π rad/s.

∆t = 0.375(s) = 3T/4. Malingana ndi nthawi yogawa nthawi, n’zosavuta kuona kuti x = – 4 cm = $-\dfrac{A\sqrt{2}}{2}$ → \cm.

Pa t = 0, chinthucho chili ndi x = $-\dfrac{A\sqrt{2}}{2}$ (+) → gawo loyambirira ndi $\varphi =-\dfrac{3\pi}{4}$.

Ndime 25.

Chinthu chimayenda molumikizana ndi nthawi ya 2 s, matalikidwe A. Nthawi yaifupi yomwe imatengera chinthu kuyenda kuchokera ku VTCB kupita ku 0.6A ndi

. 0.205s. 0.285s. 0.215s.. 0.295s.

Kugwiritsa ntchito njira yophunzirira kwa nthawi yomwe chinthucho chimayenda pakati pa VTCB ndi kusamuka kosakhazikika x ndi:

\.

Chithunzi cha 26.

Chinthu chimazungulira moyenda molumikizana ndi nthawi ya 2 s, matalikidwe A. Nthawi yayifupi kwambiri yomwe imatenga kuti chinthu chiyende kuchokera kumalire abwino kupita pamalo 0.8A ndi

. 0.285s.. 0.215s.. 0.295s. 0.205s

Kugwiritsa ntchito njira yophunzirira ya nthawi yomwe imatengera chinthu kuti chizungulire pakati pa malire ndi osakhala enieni x ndi:

\.

Chithunzi cha 27.

Chinthu chimazungulira ndi nthawi ya 2 s, matalikidwe A. Nthawi yaifupi yomwe imatenga chinthucho kuchoka pa malo 0.6A kupita kumalo -0.8A ndi

. 0.41s ku.. 0.205s. 0.5s ku.. 0.59s ku.

Njira 1

– kugwiritsa ntchito chilinganizo chophunzirira cha nthawi yapakati pakati pa chinthu pakati pa VTCB ndi digiri ya x yosadziwika ndi:

\.

→ Nthawi yopeza ndi: \

Njira 2

– kugwiritsa ntchito gawo lozungulira,

adapeza kuti nthawi yomwe imatengera chinthucho kuchoka pa malo 0.6A kupita ku malo -0.8A ndi nthawi yomwe gawolo limachokera ku P1 kupita ku P2.

Zomwe (0.6A)2 + (0.8A)2 = A2

→ \→ t = \

Ndime 28.

Chinthu chimagwedezeka ndi nthawi ya 3 s ndi matalikidwe a 20 cm. Chinthucho poyamba pa malo 10 cm ndi mbali zabwino. Ndi liti pamene chinthucho chili ndi mtunda wa 15 cm ndipo chili kumbali yabwino?

. 0.205s.. 0.155s.. 0.095s ku.. 0.345 ndi.

Nthawi yopeza ndi: $\Delta t=\Delta {{t}_{O\to 15\text{cm}}}-\Delta {{t}_{O\to \text{1}0\ text{cm}}}=T\dfrac{\arcsin \dfrac{15}{20}}{2\pi }-\dfrac{T}{12}=0,155\text{ s}$.

Onaninso: Kodi kugwiritsa ntchito kwa Be To V – Tobe To V Structure * To

Ndime 29.

Chinthu chimagwedezeka ndi nthawi ya 3 s ndi matalikidwe a 20 cm. Chinthucho poyamba pa malo 10 cm ndi mbali zabwino. Kodi ndi liti pamene chinthucho chimakhala 15 cm kutali ndi mbali yolakwika?