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.
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