Q#1: Four masses A, B, C and D carried by a rotating shaft at radii 80 mm, 100mm, 160 and 120 mm respectively are completely balanced. Masses B, C and D are 8 kg, 4 kg and 3kg respectively. Determine the mass A and the relative angular positions of the four masses if each of the plane are spaced 500 mm apart.

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Q: completely balanced

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.