The two identical cylinders of mass m, radius r, and centroidal mass moment of inertia Iˉ=2mr2 shown in Figure 1 are at
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Figure 1
The two identical cylinders of mass m, radius r, and centroidal mass moment of inertia Iˉ=2mr2 shown in Figure 1 are attached to each other and to rigid supports by springs having the stiffnesses shown. Assuming that the cylinders roll without slipping, determine: a) Differential equations of motion of the system in terms of generalised coordinates θ1 and θ2 shown in the figure. (CO2/PO3/ C4, 4 marks) b) The natural frequencies of the system using I. Eigensolution (CO2/PO3/ C4, 2 marks) II. Dunkerley's method (CO2/PO3/ C4, 2 marks) III. Rayleigh Quotient and (CO2/PO3/ C4, 2 marks) Trial Vector ={12} If m=2 kg,r=6 cm and k=300kN
Figure 1