gab t2v1.2011.1

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

restart:with(DEtools):
 
 
 edo:=diff(x(t),t,t)+3*diff(x(t),t)+2*x(t);
 
 LCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJ4RzYiNiNJInRHRitGLUYtIiIiKiYiIiRGLkYnRi5GLiomIiIjRi5GKUYuRi4=
 
 
 dsolve({edo,x(0)=1,D(x)(0)=-v});
 
 Ly1JInhHNiI2I0kidEdGJSwmKiYsJiIiIiEiIkkidkdGJUYrRistSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkKiYiIiNGK0YnRitGLEYrRisqJiwmRi1GLEY2RitGKy1GLzYjLCRGJ0YsRitGKw==
 
 
 x:=rhs(%);
 
 LCYqJiwmIiIiISIiSSJ2RzYiRiVGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKDYjLCQqJiIiI0YlSSJ0R0YoRiVGJkYlRiUqJiwmRidGJkYxRiVGJS1GKjYjLCRGMkYmRiVGJQ==
 
 
 t0:=solve(x=0,t);
 
 LCQtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYsJkkidkdGKCIiIiIiIyEiIkYtLCZGLUYvRixGLUYvRi8=
 
 
 Assim, a resposta do item (a) \303\251 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
 
 
 plot(t0,v=0..6);
 
 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
 
 
 Vemos que para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIjxGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJ2RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRjItRiw2JFEiMUYnRi9GLw== , a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPS1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYvNiVRInZGJ0YyRjVGPkY+LUYvNiNRIUYnRj4= dada pela f\303\263rmula acima assume valores negativos e assim n\303\243o satisfaz os requerimentos.
 Os valores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YyLUYsNiRRIjJGJ0YvRi8= est\303\243o fora do dom\303\255nio da fun\303\247\303\243o (aparece logaritmo de n\303\272mero negativo).
 A resposta do item (b) \303\251 a parte positiva do gr\303\241fico acima, isto \303\251:
 
 
 plot(t0,v=0..6,tzero=0..8);
 
 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
Resposta do item (c): Sim, para valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EidkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGLy9GNUY5Rjc= entre 0 e 2 a massa nunca atinge a posi\303\247\303\243o de equil\303\255brio ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=), e em particular nunca passa para o lado esquerdo ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjxGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=).
 Isto j\303\241 est\303\241 aparente do que foi feito acima, mas podemos confirmar olhando o gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== para algumas escolhas particulares de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.
 
 
 plot(subs(v=.5,x), t=0..10);
 
 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
 
 
 plot(subs(v=1.5,x), t=0..10);
 
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plot(subs(v=2.5,x), t=0..10);
 
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