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A Simple Physical Model
Another Simple Physical Model
When discussing modal synthesis, we saw that the mass-spring-damper system illustrated in Fig.
11
can be described by the differential equation
.
Figure 11:
An ideal mass-spring-damper system.
Using a simple discrete-time approximation to a derivative of the form
(
1
)
where
is the sample period, we can derive a discrete-time version of the above equation given by
(
2
)
where
and
.
The Matlab script
msd_fd.m
implements this difference equation to produce a simulated mass motion as plotted in Fig.
12
.
Figure 12:
Simulated motion of a series mass-spring-damper system using a finite difference approximation.
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.