User`s guide
110
Time Domain:
T=6 sec
Magnitude in Frequency
Domain
First Frequency:
0.167 Hz
Phase (degrees) in
Frequency Domain
Figure 31 Fourier transform result of periodic square wave with time shift.
2.3.2 Determining Damping Factor: Logarithmic Decrement
Logarithmic decrement, δ, is used to find the damping ratio of an underdamped system in
the time domain. The logarithmic decrement is the natural log of the ratio of the amplitudes of
any two successive peaks, as shown in eq.36.
where
is the amplitude of peak i (i is an integer counting each peak), n is the number of
cycles being considered, is the log decrement. If there is an offset in y, the
amplitude must be
defined relative to that offset.
The damping ratio is then found from the logarithmic decrement, as shown in eq.37.
-2
-1
0
1
2
0 2 4 6
0
0.5
1
1.5
0.0 1.0 2.0 3.0 4.0 5.0
-90
-60
-30
0
0.0 5.0 10.0 15.0 20.0 25.0 30.1 35.1 40.1