A vibratory system consists of mass m, a vertical spring of stiffness 2k and a horizontal spring of stiffness k. The end A of the horizontal spring is given a horizontal motion x_A = a sin ωt. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume m = 10 kg, k = 1.5 kN/m and neglect friction. The magnitude of the critical driving frequency for which the oscillations of mass m tend to become excessively large is _______________ rad/s (answer in integer).