lecture34[1]

lecture34[1] - Harmonic Motion (II) Mass and Spring Energy...

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1 Physics 1D03 Harmonic Motion ( II ) Serway 15.1—15.3 • Mass and Spring • Energy in SHM Practice: Chapter 15, problems 9, 15, 17, 19, 21, 67 Physics 1D03 Simple Harmonic Motion SHM: ) cos( φ ω + = t A x a(t) = - ω 2 x(t) dt dv a dt dx v = = , differentiate: and find that acceleration is proportional to displacement:

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2 Physics 1D03 Mass and Spring x m k dt x d a - = = 2 2 M x F = -kx ma kx F = - = Newton’s 2 nd Law: so This is a 2 nd order differential equation for the function x(t) . Recall that for SHM, a = -ω 2 x , identical except for the proportionality constant. So the motion of the mass will be SHM: x(t) = A cos ( ω t + φ ), and to make the equations for acceleration match, we require that m k = 2 , or m k = (and = 2 π f , etc .). Physics 1D03 Mass and Spring f (force parameter/inertia parameter) ½ The frequency is independent of amplitude . The same results hold for a mass on a vertical spring (forces are spring plus gravity), as long as the displacement is measured from the
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This note was uploaded on 12/14/2010 for the course ENGINEERIN 1D03 taught by Professor N.l.mckay during the Spring '10 term at McMaster University.

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lecture34[1] - Harmonic Motion (II) Mass and Spring Energy...

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