Unformatted text preview: A ( ω m ) = A p ( γ 2 / 2) 2 + ( ω 2γ 2 / 2) γ 2 = A p ω 2 γ 2γ 4 / 4 = A ω γ 1 q 1γ 2 4 ω 2 2. Phase Lag • Up to now we’ve focused on the amplitude of the driven oscillations: A ( ω ) • There is also physics in the phase lag: X ( t ) = A ( ω ) cos( ωtδ ); tan δ = ωγ ( ω 2ω 2 ) • The phase is a smooth connection between two regimes [see plots shown in class]: (a) At low driving frequencies δ → ◦ The mass and platform move in unison (rigid regime): X ( t ) = A cos( ωt ) for ω ± ω ◦ In this regime A ( ω ) → A ω 2 ω 2 = A ◦ The response of the system is determined by the stiffness of the spring (b) At high frequency ( ω ² ω ) A ( ω m ) = A p ( γ 2 / 2) 2 + ( ω 2γ 2 / 2) γ 2→ A ω 2 ω 2 ◦ And the phase (for ω ² ω : tan δ = ωγ ( ω 2ω 2 )→γ ω...
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 Fall '07
 PierreSavaria
 mechanics, Force, Simple Harmonic Motion, Statistical Mechanics, http://www.physics.utoronto.ca/ phy293h1f/waves/phy293 ps2.pdf

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