Physical Perspective on Repeated Poles in the Mass-Spring System
In the physical system, dc and infinite frequency are in fact strange
cases. In the case of dc, for example, a nonzero constant force
implies that the mass 
is under constant acceleration. It is
therefore the case that its velocity is linearly growing. Our
simulation predicts this, since, using
Eq.
(F.43) and Eq.(F.42),
![\begin{eqnarray*}
v_m(n) &=& \frac{f^{{+}}_m(n)}{m} - \frac{f^{{-}}_m(n)}{m}
=...
...m} \left[2(n+1) + 2n\right]x_0
= \frac{1}{m} (4 n x_0 + 2 x_0).
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/pasp/img5032.png)
The dc term 
is therefore accompanied by a linearly growing
term 
in the physical mass velocity. It is therefore
unavoidable that we have some means of producing an unbounded,
linearly growing output variable.
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Mass-Spring Boundedness in Reality
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A Signal Processing Perspective on Repeated Mass-Spring Poles
