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Transformation of stress in the plane.

",{"_44":88,"_83":89,"_85":90},"8fe73353-a58a-4aed-b557-898569cfc3c3","B","

Principal stresses and maximum shear stress in the plane.

",{"_44":92,"_83":93,"_85":94},"4ed74f68-2c6e-44c5-8df7-a81ac6f2699f","C","

Mohr's circle.

","solution_explanation","statement","

What is the topic of the lesson described in the text?

","status","pending_classification","hasRelatedVideo","relatedVideos",[103],{"_104":105,"_123":124,"_51":139,"_174":175,"_192":140},"content",{"_44":106,"_55":107,"_108":-5,"_109":110,"_111":112,"_113":-5,"_46":114,"_117":118,"_119":118,"_120":-5,"_121":122},"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",{"_115":116},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_125":126,"_132":133,"_134":135,"_136":137,"_28":138},"provider",{"_44":127,"_128":129,"_130":131},"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",[140],{"_44":141,"_55":142,"_57":143,"_144":145,"_146":-5,"_117":147,"_119":147,"_46":148,"_121":143,"_155":156},"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",{"_149":150,"_151":152,"_153":154},"childrenCount",18,"content_count",0,"question_count",135489,"children",[157],{"_44":158,"_55":159,"_57":160,"_144":145,"_146":141,"_117":161,"_119":161,"_46":162,"_121":165,"_155":166},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_149":163,"_151":152,"_153":164},10,19948,"mecanica-2",[167],{"_44":168,"_55":62,"_57":63,"_144":145,"_146":158,"_117":169,"_119":169,"_46":170,"_121":172,"_155":173},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_149":152,"_151":152,"_153":171},3376,"resistencia-dos-materiais-4",[],"video",{"_44":112,"_13":107,"_108":-5,"_176":177,"_178":179,"_28":-5,"_180":-5,"_125":179,"_181":182,"_136":-5,"_183":-5,"_184":-5,"_185":-5,"_186":-5,"_46":187,"_188":152,"_189":-5,"_98":190,"_117":191,"_119":191},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_115":116},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[195,227,245],{"_40":196,"_42":43,"_44":197,"_80":198,"_95":215,"_96":216,"_51":217},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[199,202,205,208,212],{"_44":200,"_83":84,"_85":201},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":203,"_83":89,"_85":204},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":206,"_83":93,"_85":207},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":209,"_83":210,"_85":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_44":196,"_83":213,"_85":214},"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

",[218],{"_44":219,"_55":220,"_57":221,"_144":145,"_146":222,"_117":223,"_119":223,"_46":224,"_121":221},"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",{"_149":225,"_151":152,"_153":226},4,12302,{"_40":228,"_42":43,"_44":229,"_80":230,"_95":242,"_96":243,"_51":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_44":232,"_83":84,"_85":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":235,"_83":89,"_85":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":228,"_83":93,"_85":238},"

Verdadeiro, falso, verdadeiro

",{"_44":240,"_83":210,"_85":241},"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?

",[218],{"_40":246,"_42":43,"_44":247,"_80":248,"_95":263,"_96":264,"_51":265},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[249,252,255,257,260],{"_44":250,"_83":84,"_85":251},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":253,"_83":89,"_85":254},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":246,"_83":93,"_85":256},"Indeterminado",{"_44":258,"_83":210,"_85":259},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":261,"_83":213,"_85":262},"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????",[218],[218,267,276,282,286,287,288,296,301,309,310,315,321],{"_44":268,"_55":269,"_57":270,"_144":145,"_146":271,"_117":161,"_119":161,"_46":272,"_121":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_149":273,"_151":152,"_153":274},5,30614,"engenharia-mecatronica-1",{"_44":277,"_55":62,"_57":63,"_144":145,"_146":278,"_117":279,"_119":279,"_46":280,"_121":281},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_149":152,"_151":152,"_153":171},"resistencia-dos-materiais-6",{"_44":278,"_55":159,"_57":160,"_144":145,"_146":268,"_117":223,"_119":223,"_46":283,"_121":285},{"_149":273,"_151":152,"_153":284},25741,"mecanica-3",{"_44":141,"_55":142,"_57":143,"_144":145,"_146":-5,"_117":147,"_119":147,"_46":148,"_121":143},{"_44":168,"_55":62,"_57":63,"_144":145,"_146":158,"_117":169,"_119":169,"_46":170,"_121":172},{"_44":289,"_55":290,"_57":291,"_144":145,"_146":271,"_117":161,"_119":161,"_46":292,"_121":295},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_149":293,"_151":152,"_153":294},21,45865,"engenharia-civil-3",{"_44":222,"_55":297,"_57":298,"_144":145,"_146":271,"_117":161,"_119":161,"_46":299,"_121":300},"Engenharia de Petróleo","engenharia-de-petroleo",{"_149":273,"_151":152,"_153":226},"engenharia-de-petroleo-1",{"_44":302,"_55":303,"_57":304,"_144":145,"_146":289,"_117":305,"_119":305,"_46":306,"_121":308},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_149":273,"_151":152,"_153":307},8852,"estruturas-1",{"_44":158,"_55":159,"_57":160,"_144":145,"_146":141,"_117":161,"_119":161,"_46":162,"_121":165},{"_44":311,"_55":62,"_57":63,"_144":145,"_146":219,"_117":312,"_119":312,"_46":313,"_121":314},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_149":152,"_151":152,"_153":171},"resistencia-dos-materiais-7",{"_44":316,"_55":317,"_57":63,"_144":145,"_146":302,"_117":318,"_119":318,"_46":319,"_121":320},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_149":152,"_151":152,"_153":171},"resistencia-dos-materiais-5",{"_44":271,"_55":322,"_57":323,"_144":145,"_146":-5,"_117":324,"_119":324,"_46":325,"_121":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_149":326,"_151":152,"_153":327},29,351586,"tagsTree",[140,330],{"_44":271,"_55":322,"_57":323,"_144":145,"_146":-5,"_117":324,"_119":324,"_46":325,"_121":323,"_155":331},[332,338,344],{"_44":268,"_55":269,"_57":270,"_144":145,"_146":271,"_117":161,"_119":161,"_46":272,"_121":275,"_155":333},[334],{"_44":278,"_55":159,"_57":160,"_144":145,"_146":268,"_117":223,"_119":223,"_46":283,"_121":285,"_155":335},[336],{"_44":277,"_55":62,"_57":63,"_144":145,"_146":278,"_117":279,"_119":279,"_46":280,"_121":281,"_155":337},[],{"_44":289,"_55":290,"_57":291,"_144":145,"_146":271,"_117":161,"_119":161,"_46":292,"_121":295,"_155":339},[340],{"_44":302,"_55":303,"_57":304,"_144":145,"_146":289,"_117":305,"_119":305,"_46":306,"_121":308,"_155":341},[342],{"_44":316,"_55":317,"_57":63,"_144":145,"_146":302,"_117":318,"_119":318,"_46":319,"_121":320,"_155":343},[],{"_44":222,"_55":297,"_57":298,"_144":145,"_146":271,"_117":161,"_119":161,"_46":299,"_121":300,"_155":345},[346],{"_44":219,"_55":220,"_57":221,"_144":145,"_146":222,"_117":223,"_119":223,"_46":224,"_121":221,"_155":347},[348],{"_44":311,"_55":62,"_57":63,"_144":145,"_146":219,"_117":312,"_119":312,"_46":313,"_121":314,"_155":349},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários