Oscillation Frequency
From Fig.F.33, we can see that the impedance of the parallel combination of the mass and spring is given by
(using the product-over-sum rule for combining impedances in parallel). The poles of this impedance are given by the roots of the denominator polynomial in
![$ s$](http://www.dsprelated.com/josimages_new/pasp/img144.png)
The resonance frequency of the mass-spring oscillator is therefore
Since the poles
![$ s=\pm j\omega_0$](http://www.dsprelated.com/josimages_new/pasp/img5001.png)
![$ j\omega $](http://www.dsprelated.com/josimages_new/pasp/img71.png)
We can now write reflection coefficient (see Fig.F.35) as
![$\displaystyle \rho = \frac{m-k}{m+k} = \frac{1-\frac{k}{m}}{1+\frac{k}{m}} = \frac{1-\omega_0^2}{1+\omega_0^2}
$](http://www.dsprelated.com/josimages_new/pasp/img5002.png)
![$ \omega_0=0$](http://www.dsprelated.com/josimages_new/pasp/img5003.png)
![$ \rho=1$](http://www.dsprelated.com/josimages_new/pasp/img5004.png)
![$ \omega_0=\infty$](http://www.dsprelated.com/josimages_new/pasp/img5005.png)
![$ \rho=-1$](http://www.dsprelated.com/josimages_new/pasp/img2361.png)
Next Section:
DC Analysis of the WD Mass-Spring Oscillator
Previous Section:
Checking the WDF against the Analog Equivalent Circuit