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Vibration Test: Example of
Numerical Differentiation
Prof. Dragan Djurdjanovic
ME 218
Fall 2008
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View Full Document Introduction
An instrument is
subject to a random
vibration test. The
displacement is
measured at rapid
intervals of time to
determine the velocity
and the acceleration of
the instrument. This
data is then used to
analyse stability of the
instrument.
http://www.physics.ubc.ca/~mattison/vibration/testplatform.gif
The Problem
The displacement data collected is at
discrete time instances.
Numerical differentiation techniques
need to be employed to evaluate the
velocity and the acceleration at the
desired time instances.
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View Full Document The Data
Given the data above, determine the
velocity (dy/dt) and acceleration (d
2
y/dt
2
) at
t = 0.05, 0.20 and 0.60 seconds using
suitable
finite difference formulations with
a step size of 0.05 seconds.
t
(sec)
.05
.10
.15
.20
.25
.30
.35
.40
.45
.50
.55
.60
y (in)
.144
.172
.213
.296
.070
.085
.525
.110
.062
.055
.042
.035
Solution
Since the data is known for t
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This note was uploaded on 06/23/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Unknown

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