Derive equations of motion of the planar system composed of uniform beam and a disc, two linear springs and a torsional spring. For a given data compute natural frequencies and mode shapes of small vibrations. Disregard weights of beams (g = 0). O, B - planar joints (axes). Data: Mass of beam [kg] m = 3 kg Lengths of beam [m] a = 0.8 m b = 0.7 m c = 1.4 m Mass of disc [kg], M = 6 Kg Rradius of disc [m] r = 0.4 m Stiffness coefficients of linear springs [N/m], k = 700 N/m k= 2000 N/m Stiffness coefficient of torsional spring [Nm/rad], k3= 250 Nm/rad U M,r a fun B m K3