Answer Happy

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D C 125 A1. Part of a crane can be modelled as the structure below: m is the mass of the load, ky is the stiffness of the wire rope. ki is the stiffness of a spring restraining the drum modelled as a uniform disc rotating about its centre with mass mo and radius r. as shown in Figure Al. eti) eu) * 00000 x(0) Figure A1 m= 1000 kg, ki= 200 kN/m, k2= 400 kN/m, mo = 100 kg, r = 0.25 m. The second mora moment of inertia of the disc about its centre is There is no damping 2 (a) Derive the equations of motion in terms of x and e. (8 marks) (b) Determine the natural frequencies and modes to 3 significant figures. (10 marks) (c) mis given a sudden downward impact (initial velocity (0) = 10 m/s and zero initial displacement). Determine the angle of the disc 5 seconds after the initial impact to 3 significant figures. (7 maks)