Dimensional_Analysis

Dimensional_Analysis - length l [ L ] vibrating with an...

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Dimensional Analysis Dimensional analysis is a conceptual tool often applied in physics , chemistry , and engineering to understand physical situations involving a mix of different kinds of physical quantities.
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What is the period of oscillation T of a mass m attached to an ideal linear spring with spring constant k suspended in gravity of strength g ? T [T]; m [M]; k [ M / T 2 ]; and g [ L / T 2 ]. Dimensionless number: G 1 = T 2 k / m [notice: no g!] T = k (m/k) 1/2
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Consider the case of a vibrating wire of
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Unformatted text preview: length l [ L ] vibrating with an amplitude A [ L ]. The wire has a linear density of [ M / L ] and is under tension s [ ML / T 2 ], and we want to know the energy, E [ ML 2 / T 2 ], in the wire. We can form two dimensionless products of powers of the variables chosen: 1 = E / (A s) 2 = l / A The two groups found can be combined into an equivalent form as an equation: F(E/A s, l/A) = 0 E = A s f(l/A)...
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This note was uploaded on 06/10/2011 for the course EMA 7414 taught by Professor Mecholsky during the Spring '11 term at University of Florida.

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Dimensional_Analysis - length l [ L ] vibrating with an...

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