Skip to content
Permalink
master
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?

linear_algebra/README.md

Go to file
 
 
Cannot retrieve contributors at this time
linear_algebra of segments | largest | smallest | # of eigenvalues
49 lines (39 sloc) 919 Bytes
Raw Blame
Open in GitHub Desktop

linear_algebra

size of A | norm error 3 | 4 |

  1. Solve spring mass system: M = (1 0 0 0 2 0 0 0 4) K = (k1+k2 -k2 0
    -k2 k2+k3 -k3
    0 -k3 k3+k4) K = ( 30 -20 0 -20 40 -20 0 -20 30 ) Mx'' + Kx = 0

1x1''+ 30x1 - 20x2 = 0 2x2''- 20x1 + 40x2 - 20x3 = 0 4x3''- 20x2 + 30x3 = 0

k~ = ( 30 -14.2 0 -14.2 20.16 -7.1 0 -7.1 7.5 ) (k~ - (eigenvalue)I)*v = 0 det(k~ - (eigenvalue)I) = 0 eigenvalue = E

(30-E -14.2 0 -14.2 20.16-E -7.1 = 0 0 -7.1 7.5-E)

(30-E)(((20.16-E)(7.5-E)) + 7.1(-7.1)) + 14.2(-14.2(7.5-E))

(30-E)(100.79 + 12.66E + E^2) + -1512.3 - 201.64E 3023.7 + 379.8E + 30E^2 - 100.79E - 12.66E^2 -E^3 - 1512.3 - 201.64E 1511.4 + 77.37E + 17.34E^2 -E^3 = 0

E1 = 23.4 wn1 = 4.837m/s

of segments | largest | smallest | # of eigenvalues

5 6 10