n_e = 1
String natural frequencies 
1, FEA = 8.006e+03, Exact =  7.954e+03 
Shape   0.000e+00   1.000e+00   0.000e+00 
n_e = 2
String natural frequencies 
1, FEA = 7.984e+03, Exact =  7.954e+03 
Shape   0.000e+00   7.068e-01   1.000e+00   7.068e-01   0.000e+00 
2, FEA = 1.601e+04, Exact =  1.591e+04 
Shape   0.000e+00  -1.000e+00   2.256e-16   1.000e+00   0.000e+00 
3, FEA = 2.873e+04, Exact =  2.386e+04 
Shape   0.000e+00   4.068e-01  -1.000e+00   4.068e-01   0.000e+00 
n_e = 3
String natural frequencies 
1, FEA = 7.960e+03, Exact =  7.954e+03 
Shape   0.000e+00  -5.000e-01  -8.664e-01  -1.000e+00  -8.664e-01  -5.000e-01   0.000e+00 
2, FEA = 1.608e+04, Exact =  1.591e+04 
Shape   0.000e+00   1.000e+00   9.923e-01  -1.955e-15  -9.923e-01  -1.000e+00   0.000e+00 
3, FEA = 2.402e+04, Exact =  2.386e+04 
Shape   0.000e+00   1.000e+00  -7.598e-16  -1.000e+00   3.501e-16   1.000e+00   0.000e+00 
4, FEA = 3.638e+04, Exact =  3.182e+04 
Shape   0.000e+00  -6.078e-01   1.000e+00  -2.995e-16  -1.000e+00   6.078e-01   0.000e+00 
5, FEA = 5.021e+04, Exact =  3.977e+04 
Shape   0.000e+00   3.105e-01  -1.000e+00   6.209e-01  -1.000e+00   3.105e-01   0.000e+00 
n_e = 4

String natural frequencies 
1, FEA = 7.956e+03, Exact =  7.954e+03 
Shape   0.000e+00   3.826e-01   7.071e-01   9.237e-01   1.000e+00   9.237e-01   7.071e-01   3.826e-01   0.000e+00 
2, FEA = 1.597e+04, Exact =  1.591e+04 
Shape   0.000e+00  -7.068e-01  -1.000e+00  -7.068e-01  -2.568e-15   7.068e-01   1.000e+00   7.068e-01   0.000e+00 
3, FEA = 2.426e+04, Exact =  2.386e+04 
Shape   0.000e+00   9.482e-01   7.071e-01  -3.928e-01  -1.000e+00  -3.928e-01   7.071e-01   9.482e-01   0.000e+00 
4, FEA = 3.203e+04, Exact =  3.182e+04 
Shape   0.000e+00   1.000e+00  -7.577e-16  -1.000e+00   8.894e-16   1.000e+00  -1.375e-15  -1.000e+00   0.000e+00 
5, FEA = 4.445e+04, Exact =  3.977e+04 
Shape   0.000e+00   5.653e-01  -7.071e-01  -2.342e-01   1.000e+00  -2.342e-01  -7.071e-01   5.653e-01   0.000e+00 
6, FEA = 5.745e+04, Exact =  4.772e+04 
Shape   0.000e+00  -4.068e-01   1.000e+00  -4.068e-01  -4.303e-16   4.068e-01  -1.000e+00   4.068e-01   0.000e+00 
7, FEA = 7.138e+04, Exact =  5.568e+04 
Shape   0.000e+00   1.998e-01  -7.071e-01   4.823e-01  -1.000e+00   4.823e-01  -7.071e-01   1.998e-01   0.000e+00 
quit