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# phy293 - x ” F x =-sx Hooke sLaw 1660 England 2 Equation...

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PHY293 Oscillations Lecture #1 September 11, 2009 1. Introduction/WebSite 2. Why study waves and oscillations? (see slides attached) 3. EKG demonstration ( http://faraday.physics.utoronto.ca/IYearLab/EKG.pdf ) 4. Tacoma Narrows bridge video ( http://www.youtube.com/watch?v=P0Fi1VcbpAI ) Start of material 1. Simple Harmonic Oscillations Linear resorting force Displace mass, m , spring will pull it back Assume F ( x = 0) = 0 , in other words x = 0 is equilibrium position Consider: F ( x ) = - ( sx + s 2 x 2 + s 3 x 3 + ... ) Minus sign is there to ensure the force pushes mass back to equilibrium For small enough displacements, eg: x s/s 2 ; p s/s 3 ; etc. We can ignore all but the linear term (this defines “small
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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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