Num_Differentiation_Example

Num_Differentiation_Example - Vibration Test: Example of...

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Vibration Test: Example of Numerical Differentiation Prof. Dragan Djurdjanovic ME 218 Fall 2011
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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 analyze stability of the instrument. http://www.physics.ubc.ca/~mattison/vibration/test-platform.gif
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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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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
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Solution Since the data is known for t
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Num_Differentiation_Example - Vibration Test: Example of...

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