The cross term changes the effective inertia

Consider the system of two particles with total kinetic energy T = (5/2)ẋ${}^2+l^2\theta$̇${}^2+2l$ẋ$\theta$̇$\cos \theta$, and Lagrangian L = (5/2)ẋ${}^2+l^2\theta$̇${}^2+2l$ẋ$\theta$̇$\cos \theta +2$gl $\cos \theta$, where $x,\theta$ are generalized coordinates, and g, l are positive constants. Then the non-zero frequency of the normal mode of the system with small oscillations (|$\theta$| ≪ 1) is