Figure below shows an overhead travelling crane, consisting of a girder which is simply supported at its ends, a trolley, and a wire rope. The girder is made of steel, having a span of 40 m, an area moment of inertia (I) of 0.05 m, and a modulus of elasticity (E) of 200 GPa. The trolley has a mass (mi) of 800 kg, and the load being lifted has a mass (m) of 1000 kg and the wire rope has a stiffness (k) of 500 kN/m. The system can be modelled as a two-degree-of-freedom as shown in Figure (b). a) Determine the natural frequencies of the system. b) Determine and sketch the mode shapes of the system. Girder; kg, E, I m m k Trolley Wire rope Load lifted www. m xxxxx m (b) 09 (12 marks) (8 marks)