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Unformatted text preview: 91 where I l g M O = ω 2 . The third term arises from the restoring force while the second term proportional to t d d θ represents damping . The strength of the damping is characterized by the parameter Q , called the quality factor of the system .Small Q implies large damping, while large values of Q (Q>1) represents small damping . The solution θ (t) to eq (10) can be shown to be oscillatory but with an amplitude which decreases with time as Q 2 t AO A e ) t ( ω θ θ = (11) Thus after n oscillations i.e . O 2 n T n t ω π = = the amplitude decreases from the initial amplitude θ AO by Q n O A n A e π θ θ = (12) Thus n Q ln ln AO n A π θ θ = (13) A plot of ln θ An vs n is expected to be a straight line . The quality factor can be read off from the slope . II. Setup and Procedure: Part A: Measurement of time period T for small oscillations 1 Make sure that the equilibrium position of the metal arc + magnet is at...
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 Fall '09
 LIND
 Simple Harmonic Motion, Periodic function, Arc

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