[{"_1":2,"_194":-5,"_195":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fe5d34ec-f047-49bb-a640-631d9c8c55dc","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":184,"_185":186},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":19,"_20":21,"_22":23,"_41":19,"_42":43,"_44":45},"correctOptionId","90610e81-aef9-4ffe-aace-76b69c38768f","difficulty","","id","fe5d34ec-f047-49bb-a640-631d9c8c55dc","options",[24,30,34,37],{"_20":25,"_26":27,"_28":29},"810e6928-0c0d-4244-98b8-279f9088c246","label","A","text","

2\\frac{F_0}{b_0}

",{"_20":31,"_26":32,"_28":33},"c52c357f-cbb0-4002-a321-44879cbf7f68","B","

\\frac{F_0}{2b_0}

",{"_20":17,"_26":35,"_28":36},"C","

\\frac{F_0}{b_0}

",{"_20":38,"_26":39,"_28":40},"25a1cedc-912a-44c7-afa9-65bec8c45ae0","D","

\\frac{F_0}{4b_0}

","solution_explanation","statement","

Considere as oscilações forçadas de um sistema bloco-mola amortecido. Qual a amplitude das oscilações na ressonância?

","status","pending_classification","relatedVideos",[],"similarQuestions",[50,110,127,144,164],{"_16":19,"_18":19,"_20":51,"_22":52,"_41":19,"_42":69,"_70":71},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_20":54,"_26":27,"_28":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":57,"_26":32,"_28":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":60,"_26":35,"_28":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":63,"_26":39,"_28":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":66,"_26":67,"_28":68},"112831da-be9c-458e-94cb-e8292d0dba12","E","y'' - 2y' + 6y = 0","

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

","tags",[72,95,103],{"_20":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94},"861ad829-750d-4a44-9569-2f18b430b4df","name","Engenharia Mecatrônica","alias","engenharia-mecatronica","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","metadata",{"_87":88,"_89":90,"_91":92},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_20":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":102},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_87":88,"_89":90,"_91":101},25741,"mecanica-3",{"_20":81,"_74":104,"_76":105,"_78":79,"_80":-5,"_82":106,"_84":106,"_85":107,"_93":105},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":108,"_89":90,"_91":109},29,351586,{"_16":19,"_18":19,"_20":111,"_22":112,"_41":19,"_42":125,"_70":126},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[113,116,119,122],{"_20":114,"_26":27,"_28":115},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":117,"_26":32,"_28":118},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":120,"_26":35,"_28":121},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":123,"_26":39,"_28":124},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[72,95,103],{"_16":19,"_18":19,"_20":128,"_22":129,"_41":19,"_42":142,"_70":143},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[130,133,136,139],{"_20":131,"_26":27,"_28":132},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":134,"_26":32,"_28":135},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":137,"_26":35,"_28":138},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":140,"_26":39,"_28":141},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[72,95,103],{"_16":19,"_18":19,"_20":145,"_22":146,"_41":19,"_42":162,"_70":163},"996628fc-4ac3-4821-86bd-839f86a97a6d",[147,150,153,156,159],{"_20":148,"_26":27,"_28":149},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":151,"_26":32,"_28":152},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":154,"_26":35,"_28":155},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":157,"_26":39,"_28":158},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":160,"_26":67,"_28":161},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[72,95,103],{"_16":19,"_18":19,"_20":165,"_22":166,"_41":19,"_42":182,"_70":183},"c478a46c-46a8-4942-ae14-2e79def3dda2",[167,170,173,176,179],{"_20":168,"_26":27,"_28":169},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":171,"_26":32,"_28":172},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":174,"_26":35,"_28":175},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":177,"_26":39,"_28":178},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":180,"_26":67,"_28":181},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","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????",[72,95,103],[72,95,103],"tagsTree",[187],{"_20":81,"_74":104,"_76":105,"_78":79,"_80":-5,"_82":106,"_84":106,"_85":107,"_93":105,"_188":189},"children",[190],{"_20":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94,"_188":191},[192],{"_20":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":102,"_188":193},[],"actionData","errors"]

Comentários