Unformatted text preview: x ”) F ( x ) =sx Hooke sLaw , 1660 , England 2. Equation of Motion • Newton’s Law: F = ma (1686!, England) • Gives us the following: F = ma =sx • Notation ˙ x = dx/dt ; ¨ x = d 2 x/dt 2 • Gives: m ¨ x =sx or m ¨ x + sx = 0 • Will guess the solution for this second order differential equation x = a cos( ωt + φ ) • a (Amplitude) and φ (Phase) are determined from initial conditions (must be two for a second order differential equation). • ω is the oscillation frequency that is uniquely determined by the equations of motion....
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 Fall '07
 PierreSavaria
 Physics, mechanics, Equations, Statistical Mechanics, tacoma narrows bridge, order differential equation

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