4 Figure Q4 shows a simplified ride model of a rider on a motorcycle. This model can be used to obtain information about

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4 Figure Q4 shows a simplified ride model of a rider on amotorcycle. This model can be used to obtain information about thebounce and pitch modes of the motorcycle. The total mass of therider and the motorcycle, m = 302 kg and the mass moment of inertiaabout the centre of gravity, IO = 100 kgm2 . The length of l1 = 100cm and the length of l2 = 151 cm. The stiffness of elasticity forthe rear, k1 and front suspension, k2 is 23 kN/m and 33 kN/mrespectively
(a) (b) (c) (d) (e) Suggest a suitable principal coordinate toobtain information about the bounce and pitch modes of themotorcycle. Justify your suggestion. (2 marks)
Sketch the free-body diagram of the motorcycle system based onyour suggestion in Q4(a) by using equivalent rigid body model. (2marks)
Write the equation of motion of the suggested system in matrixform. Fill in all the parameters with the known values. (3marks)
Determine the natural frequencies of the motorcycle model. (10marks)
Analyze the bounce and pitch modes of the motorcycle. Sketch themodes to support your answers. (8 marks)