W-transform for exponential stability of second order delay differential equations without damping terms

In this paper a method for studying stability of the equation x″(t)+∑i=1mai(t)x(t−τi(t))=0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x″(t)+∑i=1mai(t)x(t)=0 is not exponentially stable, the delay equation can be exponentially stable.