[{"_1":2,"_220":-5,"_221":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/c69b8f8a-a620-408c-8941-e318f092433d","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_97":98,"_99":100,"_28":183,"_205":206,"_216":217,"_218":219},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_75":76,"_91":19,"_92":93,"_94":95,"_96":14},"correctOptionId","","difficulty","id","c69b8f8a-a620-408c-8941-e318f092433d","metadata",{"_25":26,"_71":72,"_73":74},"pd",{"_27":-5,"_28":29,"_52":53,"_58":59,"_60":61,"_62":63,"_64":65,"_66":63,"_67":68,"_69":70},"area","tags",[30,36,40,44,48],{"_21":31,"_32":33,"_34":35},3265,"name","Estática","alias","estatica",{"_21":37,"_32":38,"_34":39},232077,"INGENIERIA-CIVIL","ingenieria-civil",{"_21":41,"_32":42,"_34":43},1309497,"AnálisisEstructural","analisis-estructural",{"_21":45,"_32":46,"_34":47},1309498,"ResistenciadeMateriales","resistenciade-materiales",{"_21":49,"_32":50,"_34":51},1309499,"AnálisisCinemático","analisis-cinematico","subjects",[54],{"_21":55,"_32":56,"_34":57},678643,"Análise Estrutural","analise-estrutural","materialId","122275157","answerCount",1,"isIndexable",true,"mainSubject",{"_21":55,"_32":56,"_34":57},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122378098","options",[77,83,87],{"_21":78,"_79":80,"_81":82},"0b568403-2a85-4d2c-a082-4e9329bc8327","label","A","text","sistema cinemáticamente invariable",{"_21":84,"_79":85,"_81":86},"bf7bfa3b-87ea-4b73-9110-2b0b9858d53a","B","sistema cinemáticamente variable",{"_21":88,"_79":89,"_81":90},"ece4f96c-f3b7-4d9e-a4e6-cbb0d5d934c7","C","sistema crítico","solution_explanation","statement","

Realizar el análisis cinemático del sistema mostrado, concluyendo a qué tipo de sistema pertenece:

","status","pending_classification","hasRelatedVideo","relatedVideos",[],"similarQuestions",[101,144,162],{"_18":102,"_20":19,"_21":103,"_75":104,"_91":121,"_92":122,"_28":123},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[105,108,111,114,118],{"_21":106,"_79":80,"_81":107},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":109,"_79":85,"_81":110},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":112,"_79":89,"_81":113},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":115,"_79":116,"_81":117},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_21":102,"_79":119,"_81":120},"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

",[124],{"_21":125,"_32":126,"_34":127,"_128":129,"_130":131,"_132":133,"_134":133,"_23":135,"_142":143},"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",{"_136":137,"_138":139,"_140":141},"childrenCount",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_18":145,"_20":19,"_21":146,"_75":147,"_91":159,"_92":160,"_28":161},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[148,151,154,156],{"_21":149,"_79":80,"_81":150},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":152,"_79":85,"_81":153},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":145,"_79":89,"_81":155},"

Verdadeiro, falso, verdadeiro

",{"_21":157,"_79":116,"_81":158},"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?

",[124],{"_18":163,"_20":19,"_21":164,"_75":165,"_91":180,"_92":181,"_28":182},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[166,169,172,174,177],{"_21":167,"_79":80,"_81":168},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":170,"_79":85,"_81":171},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":163,"_79":89,"_81":173},"Indeterminado",{"_21":175,"_79":116,"_81":176},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":178,"_79":119,"_81":179},"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????",[124],[124,184,193,198],{"_21":185,"_32":186,"_34":187,"_128":129,"_130":125,"_132":188,"_134":188,"_23":189,"_142":192},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_136":190,"_138":139,"_140":191},5,8852,"estruturas-1",{"_21":194,"_32":56,"_34":57,"_128":129,"_130":185,"_132":195,"_134":195,"_23":196,"_142":57},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","2025-04-29T04:00:06.9766+00:00",{"_136":139,"_138":139,"_140":197},4694,{"_21":131,"_32":199,"_34":200,"_128":129,"_130":-5,"_132":201,"_134":201,"_23":202,"_142":200},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_136":203,"_138":139,"_140":204},29,351586,"tagsTree",[207],{"_21":131,"_32":199,"_34":200,"_128":129,"_130":-5,"_132":201,"_134":201,"_23":202,"_142":200,"_208":209},"children",[210],{"_21":125,"_32":126,"_34":127,"_128":129,"_130":131,"_132":133,"_134":133,"_23":135,"_142":143,"_208":211},[212],{"_21":185,"_32":186,"_34":187,"_128":129,"_130":125,"_132":188,"_134":188,"_23":189,"_142":192,"_208":213},[214],{"_21":194,"_32":56,"_34":57,"_128":129,"_130":185,"_132":195,"_134":195,"_23":196,"_142":57,"_208":215},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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