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A realimentação unitária é uma das estruturas de controle mais utilizadas para que um determinado sistema alcance o desempenho desejado.

","status","pending_classification","hasRelatedVideo","relatedVideos",[88],{"_89":90,"_108":109,"_29":124,"_150":151,"_169":170},"content",{"_21":91,"_35":92,"_93":-5,"_94":95,"_96":97,"_98":-5,"_23":99,"_102":103,"_104":103,"_105":-5,"_106":107},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_100":101},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_110":111,"_117":118,"_119":120,"_121":122,"_6":123},"provider",{"_21":112,"_113":114,"_115":116},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[125],{"_21":126,"_35":127,"_37":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_23":133,"_106":128,"_140":141},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_134":135,"_136":137,"_138":139},"childrenCount",18,"content_count",0,"question_count",135489,"children",[142],{"_21":143,"_35":36,"_37":38,"_129":130,"_131":126,"_102":144,"_104":144,"_23":145,"_106":148,"_140":149},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_134":146,"_136":137,"_138":147},10,19948,"mecanica-2",[],"video",{"_21":97,"_152":92,"_93":-5,"_153":154,"_155":156,"_6":-5,"_157":-5,"_110":156,"_158":159,"_121":-5,"_160":-5,"_161":-5,"_162":-5,"_163":-5,"_23":164,"_165":137,"_166":-5,"_83":167,"_102":168,"_104":168},"title","duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_100":101},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_21":126,"_35":127,"_37":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_23":171,"_106":128,"_140":172},{"_134":135,"_136":137,"_138":139},[173],{"_21":143,"_35":36,"_37":38,"_129":130,"_131":126,"_102":144,"_104":144,"_23":174,"_106":148,"_140":175},{"_134":146,"_136":137,"_138":147},[],"similarQuestions",[178,208,228],{"_18":179,"_20":19,"_21":180,"_56":181,"_80":196,"_81":197,"_29":198},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[182,185,188,191,194],{"_21":183,"_60":61,"_62":184},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":186,"_60":66,"_62":187},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":189,"_60":70,"_62":190},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":192,"_60":74,"_62":193},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_21":179,"_60":78,"_62":195},"y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[199],{"_21":200,"_35":201,"_37":202,"_129":130,"_131":203,"_102":144,"_104":144,"_23":204,"_106":207},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_134":205,"_136":137,"_138":206},5,30614,"engenharia-mecatronica-1",{"_18":209,"_20":19,"_21":210,"_56":211,"_80":223,"_81":224,"_29":225},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[212,215,218,220],{"_21":213,"_60":61,"_62":214},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":216,"_60":66,"_62":217},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":209,"_60":70,"_62":219},"

Verdadeiro, falso, verdadeiro

",{"_21":221,"_60":74,"_62":222},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[226],{"_21":200,"_35":201,"_37":202,"_129":130,"_131":203,"_102":144,"_104":144,"_23":227,"_106":207},{"_134":205,"_136":137,"_138":206},{"_18":229,"_20":19,"_21":230,"_56":231,"_80":246,"_81":247,"_29":248},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[232,235,238,240,243],{"_21":233,"_60":61,"_62":234},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":236,"_60":66,"_62":237},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":229,"_60":70,"_62":239},"Indeterminado",{"_21":241,"_60":74,"_62":242},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":244,"_60":78,"_62":245},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[249],{"_21":200,"_35":201,"_37":202,"_129":130,"_131":203,"_102":144,"_104":144,"_23":250,"_106":207},{"_134":205,"_136":137,"_138":206},[252,254,260,262,264],{"_21":200,"_35":201,"_37":202,"_129":130,"_131":203,"_102":144,"_104":144,"_23":253,"_106":207},{"_134":205,"_136":137,"_138":206},{"_21":255,"_35":36,"_37":38,"_129":130,"_131":200,"_102":256,"_104":256,"_23":257,"_106":259},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_134":205,"_136":137,"_138":258},25741,"mecanica-3",{"_21":126,"_35":127,"_37":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_23":261,"_106":128},{"_134":135,"_136":137,"_138":139},{"_21":143,"_35":36,"_37":38,"_129":130,"_131":126,"_102":144,"_104":144,"_23":263,"_106":148},{"_134":146,"_136":137,"_138":147},{"_21":203,"_35":265,"_37":266,"_129":130,"_131":-5,"_102":267,"_104":267,"_23":268,"_106":266},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_134":269,"_136":137,"_138":270},29,351586,"tagsTree",[273,279],{"_21":126,"_35":127,"_37":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_23":274,"_106":128,"_140":275},{"_134":135,"_136":137,"_138":139},[276],{"_21":143,"_35":36,"_37":38,"_129":130,"_131":126,"_102":144,"_104":144,"_23":277,"_106":148,"_140":278},{"_134":146,"_136":137,"_138":147},[],{"_21":203,"_35":265,"_37":266,"_129":130,"_131":-5,"_102":267,"_104":267,"_23":280,"_106":266,"_140":281},{"_134":269,"_136":137,"_138":270},[282],{"_21":200,"_35":201,"_37":202,"_129":130,"_131":203,"_102":144,"_104":144,"_23":283,"_106":207,"_140":284},{"_134":205,"_136":137,"_138":206},[285],{"_21":255,"_35":36,"_37":38,"_129":130,"_131":200,"_102":256,"_104":256,"_23":286,"_106":259,"_140":287},{"_134":205,"_136":137,"_138":258},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários