1) A machine part having a mass of 2.5 kg implements the vibration in a viscous damping medium. A harmonic exciting force of 30 N acts on the part and causes a resonant amplitude of 14mm, with a period of 0.22 Sec. Determine the damping coefficient when the frequency of exciting force is altered to 4 Hz. Find the increase in the amplitude of forced vibration upon the removal of the damper.
2) In a vibrating system, the total mass of the system is 25 kg. At speed of system and eccentric mass have a phase difference of 90° and the corresponding amplitude is 1.5 cm. The eccentric unbalanced mass of 1 kg has a radius of rotation 4 cm. Determine:
i) The natural frequency of the system.
ii) The damping factor,
iii) The amplitude at 1500 rpm and
iv) The phase angle at 1500 rpm.
3) A shaft of diameter 10 mm carries at its centre a mass of 12 kg. It is supported by two short bearings, the centre distance of which is 400 mm. Compute the whirling speed:
a) Neglecting the mass of the shaft, and
b) Taking the mass of the shaft also into consideration.
c) The density of shaft material is 7500 kg/m^{3}.