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In this paper we introduce a numerically stable method for determining the stability of n-DOF system without computing eigenvalues. In this sense, at first we reduce the second-order system to a standard eigenvalue problem with symmetric tridiagonal form. Then we compute the exact inertia by using an algorithm based on floating point arithmetic [1]. Numerical tests report the effectiveness of these methods

Analyzing the Stability of a &lt;i&gt;n-DOF&lt;/i&gt; System with Viscous Damping

Analyzing the Stability of a <i>n-DOF</i> System with Viscous Damping