Design of Damped Free Vibration Systems
Three damped free vibrations,
overdamped, critical damped, and underdamped,
are described in Exercises in Chapter 6 Functions
in the book
C for Engineers and Scientists: An Interpretive Approach
(by Harry H. Cheng, published by McGraw-Hill, 2009).
The details for the programs using
QuickAnimation, presented below, are decribed in
QuickAnimation User's Guide.
Each of these three programs
uses Ch QuickAnimation for quick animation
of these three damped vibrations below.
One may consider the motion of the damped free vibrations below
as an elevator approaching a stop.
It would be very uncomfortable to ride if it were
underdamped, and very slow to ride if it were overdamped.
Critical damping provides the fastest and smoothest ride.
uses Ch plotting capabilities
to generate a plot shown below
for distances of these three damped vibrations.
You can see the oscillation in underdamped free vibration clearly.
uses Ch QuickAnimation to display the positions
for three vibrations
when time t is 2 seconds.