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