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are called vibrations that occur without active influence of
external forces under the action of elastic forces alone system. In
reality, as a result of free oscillations of the resistance gradually
damped and the system comes to rest. Forced oscillations occur
with the active action of external forces, mostly periodicals that
support the oscillatory motion.
Depending on the type of elastic deformation distinguish
longitudinal, shear and torsional vibrations, and depending on the
movement - small and large fluctuations.
The simplest kind of vibrations with which we deal in
engineering calculations is small harmonic oscillations, which are
described by linear differential equations with constant
coefficients.

7.3.1 Free vibrations of beams with one degree of
freedom

Consider free oscillations of weightless beam with the
attached load Q (fig.7.10 a). Static beam deflection is caused by
the load Q , will be
Q
  , (7.30)
c
where c – hardness of the beam.
Assume the coordinate axis Oy with origin at the center of
the weight of the load Q after the static displacement.

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