  Localization of normal modes is used in recent microelectromechanical systems
(MEMS) technologies with orders of magnitude improvements in sensitivity. A
pair of eigenvalues veer, or avoid crossing each other, as a single parameter
of a vibrating system is varied. While it is well-known that the sensitivity
($s$) of modal amplitude ratio varies with strength of coupling ($\kappa$) as
$s \propto\kappa^{-1} $ in the case of two identical coupled oscillators,
recently, we showed that asymmetry $\alpha$ will also influence sensitivity
according to $s \propto (\alpha \kappa)^{-1}$. Here, we show that further
enhancements in sensitivity is possible in higher degrees of freedom ($n$)
systems using energy analysis. In the case of $n-2$ uniformly coupled
oscillators embedded between two oscillators, we show that $s \propto
\alpha^{-1}\kappa^{1-n}$, if the blocked resonance spectra of the embedded
oscillators and the end oscillators are well-separated. We also show that
asymmetric coupled oscillators also enhance linear range in addition to
sensitivity when compared to their symmetric counterparts. We do not use a
perturbation approach in our energy analysis; hence the sensitivity and linear
range expressions derived have a wider range of accuracy.
