Thus, in the presence of resistance forces, the free oscillations of the system are damped. The amplitude of the oscillations in this case decreases to zero. If the resistance forces and mass are constant, then the circular frequency and period of oscillations also remain constant, depending on the elastic properties of the system. For most engineering structures, the coefficient k is small compared to the frequency of free oscillations ω. Therefore, in practical calculations, resistance forces are usually neglected and approximate values of the period and frequency of free oscillations are determined using formulas (7) and (8),instead of (22) and (23).
As a measure of oscillation damping, the so-called logarithmic decrement of oscillations is often used. It is defined as follows. At moments of time tn and tn+1 (see Fig. 10), the amplitudes of oscillations according to formula (21) will be:
The relationship of these amplitudes
Let’s denote
The dimensionless constant γ is called the logarithmic decrement of oscillations. It is also a dynamic characteristic of the system and is taken from tables available in reference literature.
