We continue to use the example introduced in
§2.1 and Figure 2.1.
We now consider the case where there are arbitrary positive masses
,
but the damping constants are zero. This simplifies the equations
of motion to
.
We again solve them by substituting
, where is
a constant vector and is a constant scalar to be determined.
This yields
Following item 3 in §2.3.7, we may convert this to a standard
Hermitian eigenvalue problem as follows. Let be the Cholesky
decomposition of . Thus is simply the diagonal matrix
. Then the eigenvalues of
are the same as the eigenvalues of the symmetric tridiagonal
matrix