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Quando os momentos de inércia são extremos (máximo / mínimo) são denominados de momentos principais.
Nessa situação, o produto de inércia é nulo.","status","pending_classification","hasRelatedVideo","relatedVideos",[110],{"_111":112,"_130":131,"_50":146,"_181":182,"_199":147},"content",{"_43":113,"_54":114,"_115":-5,"_116":117,"_118":119,"_120":-5,"_45":121,"_124":125,"_126":125,"_127":-5,"_128":129},"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",{"_122":123},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_132":133,"_139":140,"_141":142,"_143":144,"_28":145},"provider",{"_43":134,"_135":136,"_137":138},"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",[147],{"_43":148,"_54":149,"_56":150,"_151":152,"_153":-5,"_124":154,"_126":154,"_45":155,"_128":150,"_162":163},"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",{"_156":157,"_158":159,"_160":161},"childrenCount",18,"content_count",0,"question_count",135489,"children",[164],{"_43":165,"_54":166,"_56":167,"_151":152,"_153":148,"_124":168,"_126":168,"_45":169,"_128":172,"_162":173},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_156":170,"_158":159,"_160":171},10,19948,"mecanica-2",[174],{"_43":175,"_54":73,"_56":57,"_151":152,"_153":165,"_124":176,"_126":176,"_45":177,"_128":179,"_162":180},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_156":159,"_158":159,"_160":178},3376,"resistencia-dos-materiais-4",[],"video",{"_43":119,"_13":114,"_115":-5,"_183":184,"_185":186,"_28":-5,"_187":-5,"_132":186,"_188":189,"_143":-5,"_190":-5,"_191":-5,"_192":-5,"_193":-5,"_45":194,"_195":159,"_196":-5,"_105":197,"_124":198,"_126":198},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_122":123},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[202,235,253],{"_40":203,"_42":41,"_43":204,"_90":205,"_102":223,"_103":224,"_50":225},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[206,209,212,216,220],{"_43":207,"_94":95,"_96":208},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":210,"_94":100,"_96":211},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":213,"_94":214,"_96":215},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_43":217,"_94":218,"_96":219},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":203,"_94":221,"_96":222},"E","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

",[226],{"_43":227,"_54":228,"_56":229,"_151":152,"_153":230,"_124":231,"_126":231,"_45":232,"_128":229},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_156":233,"_158":159,"_160":234},4,12302,{"_40":236,"_42":41,"_43":237,"_90":238,"_102":250,"_103":251,"_50":252},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[239,242,245,247],{"_43":240,"_94":95,"_96":241},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":243,"_94":100,"_96":244},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":236,"_94":214,"_96":246},"

Verdadeiro, falso, verdadeiro

",{"_43":248,"_94":218,"_96":249},"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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[226],[226,275,284,290,294,295,296,304,309,317,318,323,329],{"_43":276,"_54":277,"_56":278,"_151":152,"_153":279,"_124":168,"_126":168,"_45":280,"_128":283},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_156":281,"_158":159,"_160":282},5,30614,"engenharia-mecatronica-1",{"_43":285,"_54":73,"_56":57,"_151":152,"_153":286,"_124":287,"_126":287,"_45":288,"_128":289},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_156":159,"_158":159,"_160":178},"resistencia-dos-materiais-6",{"_43":286,"_54":166,"_56":167,"_151":152,"_153":276,"_124":231,"_126":231,"_45":291,"_128":293},{"_156":281,"_158":159,"_160":292},25741,"mecanica-3",{"_43":148,"_54":149,"_56":150,"_151":152,"_153":-5,"_124":154,"_126":154,"_45":155,"_128":150},{"_43":175,"_54":73,"_56":57,"_151":152,"_153":165,"_124":176,"_126":176,"_45":177,"_128":179},{"_43":297,"_54":298,"_56":299,"_151":152,"_153":279,"_124":168,"_126":168,"_45":300,"_128":303},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_156":301,"_158":159,"_160":302},21,45865,"engenharia-civil-3",{"_43":230,"_54":305,"_56":306,"_151":152,"_153":279,"_124":168,"_126":168,"_45":307,"_128":308},"Engenharia de Petróleo","engenharia-de-petroleo",{"_156":281,"_158":159,"_160":234},"engenharia-de-petroleo-1",{"_43":310,"_54":311,"_56":312,"_151":152,"_153":297,"_124":313,"_126":313,"_45":314,"_128":316},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_156":281,"_158":159,"_160":315},8852,"estruturas-1",{"_43":165,"_54":166,"_56":167,"_151":152,"_153":148,"_124":168,"_126":168,"_45":169,"_128":172},{"_43":319,"_54":73,"_56":57,"_151":152,"_153":227,"_124":320,"_126":320,"_45":321,"_128":322},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_156":159,"_158":159,"_160":178},"resistencia-dos-materiais-7",{"_43":324,"_54":325,"_56":57,"_151":152,"_153":310,"_124":326,"_126":326,"_45":327,"_128":328},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_156":159,"_158":159,"_160":178},"resistencia-dos-materiais-5",{"_43":279,"_54":330,"_56":331,"_151":152,"_153":-5,"_124":332,"_126":332,"_45":333,"_128":331},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_156":334,"_158":159,"_160":335},29,351586,"tagsTree",[147,338],{"_43":279,"_54":330,"_56":331,"_151":152,"_153":-5,"_124":332,"_126":332,"_45":333,"_128":331,"_162":339},[340,346,352],{"_43":276,"_54":277,"_56":278,"_151":152,"_153":279,"_124":168,"_126":168,"_45":280,"_128":283,"_162":341},[342],{"_43":286,"_54":166,"_56":167,"_151":152,"_153":276,"_124":231,"_126":231,"_45":291,"_128":293,"_162":343},[344],{"_43":285,"_54":73,"_56":57,"_151":152,"_153":286,"_124":287,"_126":287,"_45":288,"_128":289,"_162":345},[],{"_43":297,"_54":298,"_56":299,"_151":152,"_153":279,"_124":168,"_126":168,"_45":300,"_128":303,"_162":347},[348],{"_43":310,"_54":311,"_56":312,"_151":152,"_153":297,"_124":313,"_126":313,"_45":314,"_128":316,"_162":349},[350],{"_43":324,"_54":325,"_56":57,"_151":152,"_153":310,"_124":326,"_126":326,"_45":327,"_128":328,"_162":351},[],{"_43":230,"_54":305,"_56":306,"_151":152,"_153":279,"_124":168,"_126":168,"_45":307,"_128":308,"_162":353},[354],{"_43":227,"_54":228,"_56":229,"_151":152,"_153":230,"_124":231,"_126":231,"_45":232,"_128":229,"_162":355},[356],{"_43":319,"_54":73,"_56":57,"_151":152,"_153":227,"_124":320,"_126":320,"_45":321,"_128":322,"_162":357},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários