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Figure 7.12

In this case, the differential equation of forced oscillations
of systems with one degree of freedom has the form
m  y  cy  H sin  t (7.40)
differs from the equation of free oscillations (7.31) only by the
right side.
A partial solution of the inhomogeneous equation looking
at a
y  Asin  t . (7.41)
Constant A - is the amplitude of forced oscillations. It is
determined from the condition that the partial solution (7.41)
identically satisfies the equation (7.40). From this condition we
obtain the equality
A  m  2  c sin  t  H sin  t ,
which turns into identity when
A c  m 2  H .
From the last equation we find
H 1 H 1
A     .
c m 2 c  2
1   

c 1   

  0 
The formulas for the amplitude of forced oscillations can be
written as:
H
A   . (7.42)
c
H
Size - is the static deflection of the rod under the action of a
c
maximum value H perturbing forces. Ratio  , defined as

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