When the particles of the shaft or disc moves parallel to the axis of the shaft, then the vibrations are known as longitudinal vibrations.

In transverse vibrations,the shaft is straight and bent alternately and bending stresses are induced in the shaft.

Magnificiant Factor is the ratio of maximum displacement of the forced vibration (xmax) to the deflection due to the static force F(xo).

There is a phase difference of 180° between the transmitted force and the disturbing force.

Natural Frequency, fn = 0.4985/δ

The value of ω/ωn must be greater than √2 if ε is to be less than 1 and it is the numerical value of ε , independent of any phase difference between the forces that may exist which is important.

When the roots are real, overdamping takes place.

To determine the critical speed of a shaft which may be subjected to point loads, uniformly distributed load or combination of both, we find the frequency of transverse vibration which is equal to critical speed of a shaft in r.p.s. The Dunkerley’s method may be used for calculating the frequency.

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When no external force acts on the body, after giving it an initial displacement, then the body is said to be under free or natural vibrations. The frequency of the free vibrations is called free or natural frequency.