First Order Filter
A first order filter, with cutoff frequency R, is used to identify the dynamic component, x , of the input signal, X. The transfer functions of the signal sent to the dynamic and the static models, assuming X0=0, are:
TF of signal to dynamic model =
TF of signal to dynamic model = 1
The following are Bode plots for these transfer functions:

- The top figure plots the magnitude of the transfer function against Log10(ω/R) .
- The bottom figure plots the loss angle of the transfer function against Log10(ω/R) .
- Plots of the signal sent to the dynamic model are gray-blue.
- Plots of the signal sent to the static model are brick-red.
The log scale used for the x-axis lets you view a wide range of frequencies and filter behavior as follows:
- When
(ω/R)
≪ 1, that is at low frequencies, then:
- The magnitude of the signal sent to the dynamic model is close to 0.
- The loss angle of the signal sent to the dynamic model is close to 90°.
- The magnitude of the signal sent to the static model is 1.
- The loss angle of the signal sent to the static model is 0°.
The bushing essentially behaves as the static model. The loss angle of the signal sent to the dynamic model is close to 90°, but this is not important since the magnitude of the signal is close to zero.
- When
(ω/R)
≫ 1, that is at high frequencies, then:
- The magnitude of the signal sent to the dynamic model is close to 1.
- The loss angle of the signal sent to the dynamic model is close to 0° .
- The magnitude of the signal sent to the static model is 1.
- The loss angle of the signal sent to the static model is 0°.
The bushing essentially behaves as a dynamic model superimposed on top of a static model.
- When
(ω/R)
≫ 1, that is at cut-off frequency, then:
- The magnitude of the signal sent to the dynamic model is 1/√2≈0.701 .
- The loss angle of the signal sent to the dynamic model is 45°.
- The magnitude of the signal sent to the static model is 1.
- The loss angle of the signal sent to the static model is 0°.
The bushing essentially behaves as a dynamic model superimposed on top of a static model.