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O comprimento sem deformação da mola AB é de 2m. Com o bloco mantido na posição de equilíbrio mostrada, determine a massa dele em D.

F=k\\,\theta

","status","pending_classification","hasRelatedVideo","relatedVideos",[101],{"_102":103,"_121":122,"_52":137,"_172":173,"_190":138},"content",{"_44":104,"_58":105,"_106":-5,"_107":108,"_109":110,"_111":-5,"_46":112,"_115":116,"_117":116,"_118":-5,"_119":120},"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",{"_113":114},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_123":124,"_130":131,"_132":133,"_134":135,"_28":136},"provider",{"_44":125,"_126":127,"_128":129},"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",[138],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_46":146,"_119":141,"_153":154},"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",{"_147":148,"_149":150,"_151":152},"childrenCount",18,"content_count",0,"question_count",135489,"children",[155],{"_44":156,"_58":157,"_60":158,"_142":143,"_144":139,"_115":159,"_117":159,"_46":160,"_119":163,"_153":164},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_147":161,"_149":150,"_151":162},10,19948,"mecanica-2",[165],{"_44":166,"_58":59,"_60":61,"_142":143,"_144":156,"_115":167,"_117":167,"_46":168,"_119":170,"_153":171},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_147":150,"_149":150,"_151":169},3376,"resistencia-dos-materiais-4",[],"video",{"_44":110,"_13":105,"_106":-5,"_174":175,"_176":177,"_28":-5,"_178":-5,"_123":177,"_179":180,"_134":-5,"_181":-5,"_182":-5,"_183":-5,"_184":-5,"_46":185,"_186":150,"_187":-5,"_96":188,"_115":189,"_117":189},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_113":114},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[193,225,243],{"_40":194,"_42":43,"_44":195,"_78":196,"_93":213,"_94":214,"_52":215},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[197,200,203,206,210],{"_44":198,"_81":82,"_83":199},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":201,"_81":87,"_83":202},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":204,"_81":91,"_83":205},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":207,"_81":208,"_83":209},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_44":194,"_81":211,"_83":212},"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

",[216],{"_44":217,"_58":218,"_60":219,"_142":143,"_144":220,"_115":221,"_117":221,"_46":222,"_119":219},"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",{"_147":223,"_149":150,"_151":224},4,12302,{"_40":226,"_42":43,"_44":227,"_78":228,"_93":240,"_94":241,"_52":242},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[229,232,235,237],{"_44":230,"_81":82,"_83":231},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":233,"_81":87,"_83":234},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":226,"_81":91,"_83":236},"

Verdadeiro, falso, verdadeiro

",{"_44":238,"_81":208,"_83":239},"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?

",[216],{"_40":244,"_42":43,"_44":245,"_78":246,"_93":261,"_94":262,"_52":263},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[247,250,253,255,258],{"_44":248,"_81":82,"_83":249},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":251,"_81":87,"_83":252},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":244,"_81":91,"_83":254},"Indeterminado",{"_44":256,"_81":208,"_83":257},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":259,"_81":211,"_83":260},"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????",[216],[216,265,274,280,284,285,286,294,299,307,308,313,319],{"_44":266,"_58":267,"_60":268,"_142":143,"_144":269,"_115":159,"_117":159,"_46":270,"_119":273},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_147":271,"_149":150,"_151":272},5,30614,"engenharia-mecatronica-1",{"_44":275,"_58":59,"_60":61,"_142":143,"_144":276,"_115":277,"_117":277,"_46":278,"_119":279},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_147":150,"_149":150,"_151":169},"resistencia-dos-materiais-6",{"_44":276,"_58":157,"_60":158,"_142":143,"_144":266,"_115":221,"_117":221,"_46":281,"_119":283},{"_147":271,"_149":150,"_151":282},25741,"mecanica-3",{"_44":139,"_58":140,"_60":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_46":146,"_119":141},{"_44":166,"_58":59,"_60":61,"_142":143,"_144":156,"_115":167,"_117":167,"_46":168,"_119":170},{"_44":287,"_58":288,"_60":289,"_142":143,"_144":269,"_115":159,"_117":159,"_46":290,"_119":293},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_147":291,"_149":150,"_151":292},21,45865,"engenharia-civil-3",{"_44":220,"_58":295,"_60":296,"_142":143,"_144":269,"_115":159,"_117":159,"_46":297,"_119":298},"Engenharia de Petróleo","engenharia-de-petroleo",{"_147":271,"_149":150,"_151":224},"engenharia-de-petroleo-1",{"_44":300,"_58":301,"_60":302,"_142":143,"_144":287,"_115":303,"_117":303,"_46":304,"_119":306},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_147":271,"_149":150,"_151":305},8852,"estruturas-1",{"_44":156,"_58":157,"_60":158,"_142":143,"_144":139,"_115":159,"_117":159,"_46":160,"_119":163},{"_44":309,"_58":59,"_60":61,"_142":143,"_144":217,"_115":310,"_117":310,"_46":311,"_119":312},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_147":150,"_149":150,"_151":169},"resistencia-dos-materiais-7",{"_44":314,"_58":315,"_60":61,"_142":143,"_144":300,"_115":316,"_117":316,"_46":317,"_119":318},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_147":150,"_149":150,"_151":169},"resistencia-dos-materiais-5",{"_44":269,"_58":320,"_60":321,"_142":143,"_144":-5,"_115":322,"_117":322,"_46":323,"_119":321},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_147":324,"_149":150,"_151":325},29,351586,"tagsTree",[138,328],{"_44":269,"_58":320,"_60":321,"_142":143,"_144":-5,"_115":322,"_117":322,"_46":323,"_119":321,"_153":329},[330,336,342],{"_44":266,"_58":267,"_60":268,"_142":143,"_144":269,"_115":159,"_117":159,"_46":270,"_119":273,"_153":331},[332],{"_44":276,"_58":157,"_60":158,"_142":143,"_144":266,"_115":221,"_117":221,"_46":281,"_119":283,"_153":333},[334],{"_44":275,"_58":59,"_60":61,"_142":143,"_144":276,"_115":277,"_117":277,"_46":278,"_119":279,"_153":335},[],{"_44":287,"_58":288,"_60":289,"_142":143,"_144":269,"_115":159,"_117":159,"_46":290,"_119":293,"_153":337},[338],{"_44":300,"_58":301,"_60":302,"_142":143,"_144":287,"_115":303,"_117":303,"_46":304,"_119":306,"_153":339},[340],{"_44":314,"_58":315,"_60":61,"_142":143,"_144":300,"_115":316,"_117":316,"_46":317,"_119":318,"_153":341},[],{"_44":220,"_58":295,"_60":296,"_142":143,"_144":269,"_115":159,"_117":159,"_46":297,"_119":298,"_153":343},[344],{"_44":217,"_58":218,"_60":219,"_142":143,"_144":220,"_115":221,"_117":221,"_46":222,"_119":219,"_153":345},[346],{"_44":309,"_58":59,"_60":61,"_142":143,"_144":217,"_115":310,"_117":310,"_46":311,"_119":312,"_153":347},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários