Modelado de las Ecuaciones Diferenciales Forzadas
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<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Implementaci\303\263n con Componentes</Font></Text-field>
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Instrucciones: Fije bien las condiciones iniciales, finalmente m, \316\262 y \316\272
Ingrese las constantes m, \316\262 y \316\272:
m = use DocumentTools in
v_masa:=Do(%masa):
v_beta:=Do(%beta):
v_kapa:=Do(%kapa):
v_ft:=Do(%ft):
eqdo:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t)-v_ft=0;
eqdo_v:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t);
tiempo:=Do(%t):
val_der:=Do(%der):
v_pos:=Do(%pos):
v_der:=Do(%der):
c_i:=x(tiempo)=v_pos, D(x)(tiempo)=v_der:
solcn:=dsolve({c_i,eqdo}):
Do(%out_soluc=evalf(rhs(solcn),5)):
pos:=plot(rhs(solcn),t=0..8*Pi,color=red):
vel:=plot(diff(rhs(solcn),t),t=0..8*Pi,color=green):
acel:=plot(diff(rhs(solcn),t$2),t=0..8*Pi,color=blue):
#Do(%Plot0=plot(graf,t=0..20)):
Do(%Plot0=display({pos,vel,acel},title="Posici\303\263n_Velocidad_Aceleraci\303\263n vs Tiempo", legend = ["Posici\303\263n","Velocidad","Aceleraci\303\263n"]));
Do(%out_edo=eqdo_v);
Do(%vel_e=evalf(diff(rhs(solcn),t)),5);
Do(%acel_e=evalf(diff(rhs(solcn),t$2)),5);
end use;
, \316\262 = use DocumentTools in
v_masa:=Do(%masa):
v_beta:=Do(%beta):
v_kapa:=Do(%kapa):
v_ft:=Do(%ft):
eqdo:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t)-v_ft=0;
eqdo_v:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t);
tiempo:=Do(%t):
val_der:=Do(%der):
v_pos:=Do(%pos):
v_der:=Do(%der):
c_i:=x(tiempo)=v_pos, D(x)(tiempo)=v_der:
solcn:=dsolve({c_i,eqdo}):
Do(%out_soluc=evalf(rhs(solcn),5)):
pos:=plot(rhs(solcn),t=0..8*Pi,color=red):
vel:=plot(diff(rhs(solcn),t),t=0..8*Pi,color=green):
acel:=plot(diff(rhs(solcn),t$2),t=0..8*Pi,color=blue):
#Do(%Plot0=plot(graf,t=0..20)):
Do(%Plot0=display({pos,vel,acel},title="Posici\303\263n_Velocidad_Aceleraci\303\263n vs Tiempo", legend = ["Posici\303\263n","Velocidad","Aceleraci\303\263n"]));
Do(%out_edo=eqdo_v);
Do(%vel_e=evalf(diff(rhs(solcn),t)),5);
Do(%acel_e=evalf(diff(rhs(solcn),t$2)),5);
end use;
, \316\272 = use DocumentTools in
v_masa:=Do(%masa):
v_beta:=Do(%beta):
v_kapa:=Do(%kapa):
v_ft:=Do(%ft):
eqdo:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t)-v_ft=0;
eqdo_v:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t);
tiempo:=Do(%t):
val_der:=Do(%der):
v_pos:=Do(%pos):
v_der:=Do(%der):
c_i:=x(tiempo)=v_pos, D(x)(tiempo)=v_der:
solcn:=dsolve({c_i,eqdo}):
Do(%out_soluc=evalf(rhs(solcn),5)):
pos:=plot(rhs(solcn),t=0..8*Pi,color=red):
vel:=plot(diff(rhs(solcn),t),t=0..8*Pi,color=green):
acel:=plot(diff(rhs(solcn),t$2),t=0..8*Pi,color=blue):
#Do(%Plot0=plot(graf,t=0..20)):
Do(%Plot0=display({pos,vel,acel},title="Posici\303\263n_Velocidad_Aceleraci\303\263n vs Tiempo", legend = ["Posici\303\263n","Velocidad","Aceleraci\303\263n"]));
Do(%out_edo=eqdo_v);
Do(%vel_e=evalf(diff(rhs(solcn),t)),5);
Do(%acel_e=evalf(diff(rhs(solcn),t$2)),5);
end use;
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Visualizando la Ecuaci\303\263n Diferencial Forzada : = Selecciona f(t),sin(t),5*t,5,0,cos(t),exp(t),exp(t)*cos(t),t*sin(t),2*t^2+tuse DocumentTools in
v_masa:=Do(%masa):
v_beta:=Do(%beta):
v_kapa:=Do(%kapa):
v_ft:=Do(%ft):
eqdo:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t)-v_ft=0;
tiempo:=Do(%t):
val_der:=Do(%der):
v_pos:=Do(%pos):
v_der:=Do(%der):
c_i:=x(tiempo)=v_pos, D(x)(tiempo)=v_der:
solcn:=dsolve({c_i,eqdo}):
Do(%out_soluc=evalf(rhs(solcn),5)):
pos:=plot(rhs(solcn),t=0..8*Pi,color=red):
vel:=plot(diff(rhs(solcn),t),t=0..8*Pi,color=green):
acel:=plot(diff(rhs(solcn),t$2),t=0..8*Pi,color=blue):
#Do(%Plot0=plot(graf,t=0..20)):
Do(%Plot0=display({pos,vel,acel},title="Posici\303\263n_Velocidad_Aceleraci\303\263n vs Tiempo", legend = ["Posici\303\263n","Velocidad","Aceleraci\303\263n"]));
Do(%vel_e=evalf(diff(rhs(solcn),t)),5);
Do(%acel_e=evalf(diff(rhs(solcn),t$2)),5);
end use;
x( use DocumentTools in
v_masa:=Do(%masa):
v_beta:=Do(%beta):
v_kapa:=Do(%kapa):
v_ft:=Do(%ft):
eqdo:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t)-v_ft=0;
tiempo:=Do(%t):
val_der:=Do(%der):
v_pos:=Do(%pos):
v_der:=Do(%der):
c_i:=x(tiempo)=v_pos, D(x)(tiempo)=v_der:
solcn:=dsolve({c_i,eqdo}):
Do(%out_soluc=evalf(rhs(solcn),5)):
pos:=plot(rhs(solcn),t=0..8*Pi,color=red):
vel:=plot(diff(rhs(solcn),t),t=0..8*Pi,color=green):
acel:=plot(diff(rhs(solcn),t$2),t=0..8*Pi,color=blue):
#Do(%Plot0=plot(graf,t=0..20)):
Do(%Plot0=display({pos,vel,acel},title="Posici\303\263n_Velocidad_Aceleraci\303\263n vs Tiempo", legend = ["Posici\303\263n","Velocidad","Aceleraci\303\263n"]));
Do(%vel_e=evalf(diff(rhs(solcn),t)),5);
Do(%acel_e=evalf(diff(rhs(solcn),t$2)),5);
end use;
) = Unidad de longitud , D(x)(t) = use DocumentTools in
v_masa:=Do(%masa):
v_beta:=Do(%beta):
v_kapa:=Do(%kapa):
v_ft:=Do(%ft):
eqdo:=v_masa*diff(x(t),t$2)+v_beta*diff(x(t),t)+v_kapa*x(t)-v_ft=0;
tiempo:=Do(%t):
val_der:=Do(%der):
v_pos:=Do(%pos):
v_der:=Do(%der):
c_i:=x(tiempo)=v_pos, D(x)(tiempo)=v_der:
solcn:=dsolve({c_i,eqdo}):
Do(%out_soluc=evalf(rhs(solcn),5)):
pos:=plot(rhs(solcn),t=0..8*Pi,color=red):
vel:=plot(diff(rhs(solcn),t),t=0..8*Pi,color=green):
acel:=plot(diff(rhs(solcn),t$2),t=0..8*Pi,color=blue):
#Do(%Plot0=plot(graf,t=0..20)):
Do(%Plot0=display({pos,vel,acel},title="Posici\303\263n_Velocidad_Aceleraci\303\263n vs Tiempo", legend = ["Posici\303\263n","Velocidad","Aceleraci\303\263n"]));
Do(%vel_e=evalf(diff(rhs(solcn),t)),5);
Do(%acel_e=evalf(diff(rhs(solcn),t$2)),5);
end use;
Unidad de velocidad use DocumentTools in
Do(%masa(value)=1);
Do(%beta(value)=0);
Do(%kapa(value)=0);
Do(%out_edo=NULL);
#Do(%pos=NULL);
#Do(%ft=NULL);
#Do(%t(value)=0);
#Do(%der(value)=0);
Do(%out_soluc=NULL);
Do(%vel_e=NULL);
Do(%acel_e=NULL);
Do(%Plot0=plots[display](plots[textplot]([0,0,""]),axes=none));
end use;
Posici\303\263n =
Velocidad =
Aceleraci\303\263n =
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