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20_Mech_Reson

# 20_Mech_Reson - INDIANA UNIVERSITY DEPARTMENT OF PHYSICS...

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Unformatted text preview: INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY Laboratory #20: Mechanical Resonance Goal: Study a driven, harmonic oscillator, resonance behavior, and the effect of damping.. Equipment: Driven harmonic motion analyzer, PASCO ME-9210A, assorted springs and masses. (A) Physics: Given a mass m on a spring. The spring provides a restoring force F = &kx towards the equilibrium position at x =0, where k is the spring constant. Friction (in our case) is proportional to the velocity dx/dt . This yields the following equation of motion 2 2 = + + x m k dt dx dt x d γ . (1) The solution of this equation, t e t x t x t x t 2 max cos ) ( cos ) ( ω ω γ − ⋅ = = = , (2) describes an oscillation with a frequency of ω o =2 π f o , where ω o 2 =k/m , and with an amplitude x max that decays exponentially with time t . The energy U of the system is given by U=‰ k x max 2 , i.e., proportional to the square of the amplitude. A quantity that is often used when describing oscillations is the...
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20_Mech_Reson - INDIANA UNIVERSITY DEPARTMENT OF PHYSICS...

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