Necessary and sufficient conditions are obtained for the stability of the following second order linear system:
$x˙=θ(t)x,θ(t)=θt+∑i=1lTi$
and

$=A2,T1

$⋮$

$=Al,∑i=1l−1Ti
in terms of the eigenvalues and elements of the matrices Ai, i = 1, 2…l. The conditions become very simple for the case that l = 2. An example of a pendulum with a vibrating support is included.
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