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8 Each road wheel of a motor cycle is of 60 cm diameter and has a moment of inertia of (10)
1.2 kg-m’. The motor cycle and the rider together weighs 250 kg and the combined
centre of gravity is 65 cm above the ground level when the motor cycle is upright. The
moment ofinertia of the rotating parts of the engine is 0.18 kg-m*. The engine rotates
4.5 times the speed of the road wheel in the same sense. Find the angle of heel
necessary when the motor cycle is taking a turn of 40 m radius at a speed of 70kmph

PART ^
Answer any fourfull questions, each carries Z 0 marks.

9 a) By neglecting the mass of the slender uniform rod is shown in Fig. 4(a), (5
determine natural frequency of free vibration of the mass for small oscillations )

Fig. 4 (a) An oscillating pendulum
b)
Find the frequency of the oscillations of the system shown in Fig. 40). The roller
rolls on the surface without slipping.

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Fig. 4(b) A Cylinder rolling on a floor

10 A mass of 4.5 kg, hangs from a spring and makes damped vibration. The time of 50 (10)
complete oscillations is found to be 18 seconds and the ratio of first down ward
displacement to the sixth is found to be 2.5. http://www.ktuonline.com Find (1) the
natural frequency of the system,

(11) the stiffness of the spring in KN/m,
(iii) the damping coefficient in N-s/m,
(iv) the critical damping coefficient.

An electric motor weighing 100 kg is supported on isolators having a damping factor (10)
I of 0.2. It runs at a speed of 1500 rpm and has a rotating unbalance of 10 kgem. What

should be the stiffness of the isolators if the forces transmitted to the foundation is
| to be less than 10 % of the Imbalanced force

12 A rotor has a mass of 12 kg and mounted midway on a 24 mm diameter horizontal (10)
shaft supported at ends by bearings. The bearings are I m apart. The shaft rotates at