2.4 Free Damped Vibration of Sdf System
31
Fig. 2.14 Damped motion
Fig. 2.15 All possible SDF
systems
Time period for damped free vibration is
T d =
2π
p 2 − n 2
=
2π
p
1
1 −
n
p
2
(2.34)
Equation (2.34) reveals that the damped time period is more than the undamped
time period, but n is usually a small quantity in comparison with p. This increase
is a small quantity of second order. Therefore, for all practical purposes, it can be
assumed with sufficient accuracy that a small viscous damping does not affect the
period of vibration.
Timewise variation of the displacement for different systems has been shown
in Fig. 2.15, so that a relative idea of the displacements in different cases can be
obtained.
Example 2.7 A mass 1 kg is attached to the end of a spring with a stiffness 0.7
kN/mm. Determine the critical damping constant.
31
Fig. 2.14 Damped motion
Fig. 2.15 All possible SDF
systems
Time period for damped free vibration is
T d =
2π
p 2 − n 2
=
2π
p
1
1 −
n
p
2
(2.34)
Equation (2.34) reveals that the damped time period is more than the undamped
time period, but n is usually a small quantity in comparison with p. This increase
is a small quantity of second order. Therefore, for all practical purposes, it can be
assumed with sufficient accuracy that a small viscous damping does not affect the
period of vibration.
Timewise variation of the displacement for different systems has been shown
in Fig. 2.15, so that a relative idea of the displacements in different cases can be
obtained.
Example 2.7 A mass 1 kg is attached to the end of a spring with a stiffness 0.7
kN/mm. Determine the critical damping constant.