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← Revision 3 as of 2010-08-10 13:03:29 ⇥
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| t=var('t') I=function('I',t) DE = 5*diff(diff(I,t),t) + 20*diff(I,t) + 100*I - 425*40*cos(40*t) I(t)=desolve (DE,[I,t]) I(0)==0 de(t)=diff(I,t) de(0)==0 k1,k2=var('k1,k2') solve([I(0)==0, de(0)==0],k1,k2) print I.subs(k1=30, k2=-10) |
R,L,C,E0,a,b,omega,k=var('R,L,C,E0,a,b,omega,k') S=L*omega - 1/(omega*C) I(t)=a*cos(omega*t)+b*sin(omega*t) I(t)=I(t).subs(a=-(E0*S)/(R^2+S^2),b=(E0*R)/(R^2+S^2)) solve([L*k^2+R*k+1/C==0],k) c1,c2,d1,d2=var('c1,c2,d1,d2') I=c1*e^(d1*t)+c2*e^(d2*t)+ I(t) I=I.subs(d1=-1/2*(C*R + sqrt(C^2*R^2 - 4*C*L))/(C*L),d2=-1/2*(C*R - sqrt(C^2*R^2 - 4*C*L))/(C*L)) I=I.subs(R=20,L=5,C=1/100,E0=425,omega=4) print 'I is' print I |
Book
Advanced Engineering Mathematics
Author
Erwin Kreyszig
Edition
8th Edition
R,L,C,E0,a,b,omega,k=var('R,L,C,E0,a,b,omega,k')
S=L*omega - 1/(omega*C)
I(t)=a*cos(omega*t)+b*sin(omega*t)
I(t)=I(t).subs(a=-(E0*S)/(R^2+S^2),b=(E0*R)/(R^2+S^2))
solve([L*k^2+R*k+1/C==0],k)
c1,c2,d1,d2=var('c1,c2,d1,d2')
I=c1*e^(d1*t)+c2*e^(d2*t)+ I(t)
I=I.subs(d1=-1/2*(C*R + sqrt(C^2*R^2 - 4*C*L))/(C*L),d2=-1/2*(C*R - sqrt(C^2*R^2 - 4*C*L))/(C*L))
I=I.subs(R=20,L=5,C=1/100,E0=425,omega=4)
print 'I is'
print I
Solution by:
- Lokesh Pimpale, Student, IISER Pune
- Hardik Gajera, Student, IISER Pune