[{"_1":2,"_206":-5,"_207":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/b7381cd5-0fc2-4a28-ae1f-1ae2b14046cb","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_85":86,"_87":88,"_28":169,"_191":192,"_202":203,"_204":205},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_55":56,"_79":19,"_80":81,"_82":83,"_84":14},"correctOptionId","","difficulty","id","b7381cd5-0fc2-4a28-ae1f-1ae2b14046cb","metadata",{"_25":26,"_51":52,"_53":54},"pd",{"_27":-5,"_28":29,"_30":31,"_38":39,"_40":41,"_42":43,"_44":45,"_46":14,"_47":48,"_49":50},"area","tags",[],"subjects",[32],{"_21":33,"_34":35,"_36":37},678643,"name","Análise Estrutural","alias","analise-estrutural","materialId","122051191","answerCount",1,"isIndexable",true,"mainSubject",{"_21":33,"_34":35,"_36":37},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","121545132","options",[57,63,67,71,75],{"_21":58,"_59":60,"_61":62},"49c98e35-de99-4793-a420-9045a15722fd","label","A","text","4",{"_21":64,"_59":65,"_61":66},"8005e8e1-bc20-4953-8375-10fb7a23ef89","B","3",{"_21":68,"_59":69,"_61":70},"7e8caa23-84c6-468a-9243-911b922cbacd","C","2",{"_21":72,"_59":73,"_61":74},"af79d717-5f3b-4e68-8d74-72d291a1f293","D","1",{"_21":76,"_59":77,"_61":78},"2755b3b8-46e3-41fe-8843-8ec11847e16e","E","0","solution_explanation","statement","

Quantas rótulas precisam ser colocadas em um pórtico plano composto por duas colunas e uma viga, engastado nas bases, de modo que ele tenha um grau de hiperestaticidade igual a 1?

","status","pending_classification","hasRelatedVideo","relatedVideos",[],"similarQuestions",[89,130,148],{"_18":90,"_20":19,"_21":91,"_55":92,"_79":107,"_80":108,"_28":109},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[93,96,99,102,105],{"_21":94,"_59":60,"_61":95},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":97,"_59":65,"_61":98},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":100,"_59":69,"_61":101},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":103,"_59":73,"_61":104},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_21":90,"_59":77,"_61":106},"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

",[110],{"_21":111,"_34":112,"_36":113,"_114":115,"_116":117,"_118":119,"_120":119,"_23":121,"_128":129},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","created_at","2025-04-29T02:19:12.828432+00:00","updated_at",{"_122":123,"_124":125,"_126":127},"childrenCount",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_18":131,"_20":19,"_21":132,"_55":133,"_79":145,"_80":146,"_28":147},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[134,137,140,142],{"_21":135,"_59":60,"_61":136},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":138,"_59":65,"_61":139},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":131,"_59":69,"_61":141},"

Verdadeiro, falso, verdadeiro

",{"_21":143,"_59":73,"_61":144},"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?

",[110],{"_18":149,"_20":19,"_21":150,"_55":151,"_79":166,"_80":167,"_28":168},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[152,155,158,160,163],{"_21":153,"_59":60,"_61":154},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":156,"_59":65,"_61":157},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":149,"_59":69,"_61":159},"Indeterminado",{"_21":161,"_59":73,"_61":162},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":164,"_59":77,"_61":165},"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????",[110],[110,170,179,184],{"_21":171,"_34":172,"_36":173,"_114":115,"_116":111,"_118":174,"_120":174,"_23":175,"_128":178},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_122":176,"_124":125,"_126":177},5,8852,"estruturas-1",{"_21":180,"_34":35,"_36":37,"_114":115,"_116":171,"_118":181,"_120":181,"_23":182,"_128":37},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","2025-04-29T04:00:06.9766+00:00",{"_122":125,"_124":125,"_126":183},4694,{"_21":117,"_34":185,"_36":186,"_114":115,"_116":-5,"_118":187,"_120":187,"_23":188,"_128":186},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_122":189,"_124":125,"_126":190},29,351586,"tagsTree",[193],{"_21":117,"_34":185,"_36":186,"_114":115,"_116":-5,"_118":187,"_120":187,"_23":188,"_128":186,"_194":195},"children",[196],{"_21":111,"_34":112,"_36":113,"_114":115,"_116":117,"_118":119,"_120":119,"_23":121,"_128":129,"_194":197},[198],{"_21":171,"_34":172,"_36":173,"_114":115,"_116":111,"_118":174,"_120":174,"_23":175,"_128":178,"_194":199},[200],{"_21":180,"_34":35,"_36":37,"_114":115,"_116":171,"_118":181,"_120":181,"_23":182,"_128":37,"_194":201},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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