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Uma coluna retangular feita de aço (E=170 \text{ GPa}, \u0003C3_e=210 \text{ MPa}) possui 5,5 metros de altura. Para o caso de uma extremidade engastada e presa por pinos, você deve selecionar qual o menor perfil (base x altura) para suportar uma carga de 45 \text{ kN}. Verifique também a tensão crítica.

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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

",[230],{"_43":231,"_56":232,"_58":233,"_149":150,"_151":234,"_122":235,"_124":235,"_45":236,"_126":233},"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",{"_154":237,"_156":157,"_158":238},4,12302,{"_40":240,"_42":41,"_43":241,"_76":242,"_100":254,"_101":255,"_50":256},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[243,246,249,251],{"_43":244,"_80":81,"_82":245},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":247,"_80":86,"_82":248},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":240,"_80":90,"_82":250},"

Verdadeiro, falso, verdadeiro

",{"_43":252,"_80":94,"_82":253},"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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[280],{"_43":231,"_56":232,"_58":233,"_149":150,"_151":234,"_122":235,"_124":235,"_45":281,"_126":233},{"_154":237,"_156":157,"_158":238},[283,285,294,300,304,306,308,316,321,329,331,336,342],{"_43":231,"_56":232,"_58":233,"_149":150,"_151":234,"_122":235,"_124":235,"_45":284,"_126":233},{"_154":237,"_156":157,"_158":238},{"_43":286,"_56":287,"_58":288,"_149":150,"_151":289,"_122":166,"_124":166,"_45":290,"_126":293},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_154":291,"_156":157,"_158":292},5,30614,"engenharia-mecatronica-1",{"_43":295,"_56":57,"_58":59,"_149":150,"_151":296,"_122":297,"_124":297,"_45":298,"_126":299},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-6",{"_43":296,"_56":164,"_58":165,"_149":150,"_151":286,"_122":235,"_124":235,"_45":301,"_126":303},{"_154":291,"_156":157,"_158":302},25741,"mecanica-3",{"_43":146,"_56":147,"_58":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":305,"_126":148},{"_154":155,"_156":157,"_158":159},{"_43":173,"_56":57,"_58":59,"_149":150,"_151":163,"_122":174,"_124":174,"_45":307,"_126":177},{"_154":157,"_156":157,"_158":176},{"_43":309,"_56":310,"_58":311,"_149":150,"_151":289,"_122":166,"_124":166,"_45":312,"_126":315},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_154":313,"_156":157,"_158":314},21,45865,"engenharia-civil-3",{"_43":234,"_56":317,"_58":318,"_149":150,"_151":289,"_122":166,"_124":166,"_45":319,"_126":320},"Engenharia de Petróleo","engenharia-de-petroleo",{"_154":291,"_156":157,"_158":238},"engenharia-de-petroleo-1",{"_43":322,"_56":323,"_58":324,"_149":150,"_151":309,"_122":325,"_124":325,"_45":326,"_126":328},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_154":291,"_156":157,"_158":327},8852,"estruturas-1",{"_43":163,"_56":164,"_58":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":330,"_126":170},{"_154":168,"_156":157,"_158":169},{"_43":332,"_56":57,"_58":59,"_149":150,"_151":231,"_122":333,"_124":333,"_45":334,"_126":335},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-7",{"_43":337,"_56":338,"_58":59,"_149":150,"_151":322,"_122":339,"_124":339,"_45":340,"_126":341},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-5",{"_43":289,"_56":343,"_58":344,"_149":150,"_151":-5,"_122":345,"_124":345,"_45":346,"_126":344},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_154":347,"_156":157,"_158":348},29,351586,"tagsTree",[351,360],{"_43":146,"_56":147,"_58":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":352,"_126":148,"_160":353},{"_154":155,"_156":157,"_158":159},[354],{"_43":163,"_56":164,"_58":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":355,"_126":170,"_160":356},{"_154":168,"_156":157,"_158":169},[357],{"_43":173,"_56":57,"_58":59,"_149":150,"_151":163,"_122":174,"_124":174,"_45":358,"_126":177,"_160":359},{"_154":157,"_156":157,"_158":176},[],{"_43":289,"_56":343,"_58":344,"_149":150,"_151":-5,"_122":345,"_124":345,"_45":361,"_126":344,"_160":362},{"_154":347,"_156":157,"_158":348},[363,372,381],{"_43":286,"_56":287,"_58":288,"_149":150,"_151":289,"_122":166,"_124":166,"_45":364,"_126":293,"_160":365},{"_154":291,"_156":157,"_158":292},[366],{"_43":296,"_56":164,"_58":165,"_149":150,"_151":286,"_122":235,"_124":235,"_45":367,"_126":303,"_160":368},{"_154":291,"_156":157,"_158":302},[369],{"_43":295,"_56":57,"_58":59,"_149":150,"_151":296,"_122":297,"_124":297,"_45":370,"_126":299,"_160":371},{"_154":157,"_156":157,"_158":176},[],{"_43":309,"_56":310,"_58":311,"_149":150,"_151":289,"_122":166,"_124":166,"_45":373,"_126":315,"_160":374},{"_154":313,"_156":157,"_158":314},[375],{"_43":322,"_56":323,"_58":324,"_149":150,"_151":309,"_122":325,"_124":325,"_45":376,"_126":328,"_160":377},{"_154":291,"_156":157,"_158":327},[378],{"_43":337,"_56":338,"_58":59,"_149":150,"_151":322,"_122":339,"_124":339,"_45":379,"_126":341,"_160":380},{"_154":157,"_156":157,"_158":176},[],{"_43":234,"_56":317,"_58":318,"_149":150,"_151":289,"_122":166,"_124":166,"_45":382,"_126":320,"_160":383},{"_154":291,"_156":157,"_158":238},[384],{"_43":231,"_56":232,"_58":233,"_149":150,"_151":234,"_122":235,"_124":235,"_45":385,"_126":233,"_160":386},{"_154":237,"_156":157,"_158":238},[387],{"_43":332,"_56":57,"_58":59,"_149":150,"_151":231,"_122":333,"_124":333,"_45":388,"_126":335,"_160":389},{"_154":157,"_156":157,"_158":176},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários