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f11smid1 - m ¨ x = k x ¨ x = k m x = ω 2 x 1.3 Solution...

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SOLUTIONS MIDTERM PHY 4936 (Fall 2011) PROBLEM 1 1.1 The Lagrangian is L = 1 2 m ˙ x 2 - 1 2 k x 2 . 1.2 Euler-Lagrange equation d dt ∂L ˙ x = ∂L ∂x
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Unformatted text preview: m ¨ x = k x ¨ x = k m x = ω 2 x 1.3 Solution: x ( t ) = x cos( ω t ) + ˙ x ω sin( ω t ) ....
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