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F192023 Pages:3

PART ட்‌
Answer any four full questions, each carries 10 marks.
From fundamentals derive the expression for logarithmic decrement for a

free damped longitudinal vibration system.

Derive the formula for natural frequency of free undamped longitudinal vibration
using any 2 methods. Also derive formula for natural frequency of free transverse
vibration.

A machine of mass 75kg is mounted on springs and is fitted with a dashpot to
damp out vibrations. There are three springs each of stiffness 1ON/mm and it is
found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two
complete oscillations. Assuming that the damping force varies as the velocity,
determine : 1. The resistance of the dashpot at unit velocity. 2. The ratio of the
frequency of the damped vibration to the frequency of the undamped vibration.

3. The periodic time of the damped vibration.

A shaft 1.5 m long, supported in flexible bearings at the ends carries two wheels
each of 50 kg mass. One wheel is situated at the centre of the shaft and the other
at a distance of 375 mm from the centre towards left. The shaft is hollow of
external diameter 75 mm and internal diameter 40 mm. The density of the shaft
material is 7700 kg/m? and its modulus of elasticity is 200 GN/m’. Find the
lowest whirling speed of the shaft, taking into account the mass of the shaft.

A steel shaft 1.5m long is 95 mm in diameter for the first 0.6 m of its length,
60mm in diameter for the next 0.5n of the length and 50 mm in diameter for the
remaining 0.4m of its length. The shaft carries two flywheels at two ends, the
first having mass of 900kg and 0.85 m radius of gyration located at the 95mm
diameter end and the second having a mass of 700kg and 0.55m radius of
gyration located at the end. Determine the location of the node and the natural
frequency of free torsional vibration of the system. The modulus of rigidity of
shaft material may be taken as 8061/13

What do you understand by vibration pickups? With neat diagram explain the

working of a seismometer.

اد بد ‎TBR‏

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