PHY293 Oscillations Lecture #4September 18, 20091. First problem set ( http://www.physics.utoronto.ca/ phy293h1f/waves/phy293ps1.pdf ) Due Monday at 5:00pm2. Flash Demo ( http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/DampedSHM/DampedSHM.swf )Start of material1. Quality of an Oscillator•The equation of motion:¨x+γ˙x+ω20x= 0has two quantities with dimensions of 1/time:ω0andγ•Their ratio is dimensionless:Q=ω0γknown as theQualityof the oscillator•WhenQis large the dissipation is small and the oscillations continue for a long time.•Number of oscillations a system undergoes ’til energy falls toe-1of its original value (about 37%) is:2πnosc=ω0te•Whereteis the e-folding time thus:nosc=ω0γ12π=Q2π•Note: last substitutions only holds for large Q (whenω0≈ω0)•In terms of enegyQis related to the ratio: energy stored in oscillator/energy lost per cycleEΔE=E2πγω0E=Q2π2. Overdamped Solution•Consider the other cases:x=C
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