phy293_l06.page2 - • The rate of energy flow is called...

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Unformatted text preview: • The rate of energy flow is called power given by: P = ~ F · ~v • Looking back at the SHO equation of motion we have: ¨ x + γ ˙ x + ω 2 x = a ω 2 cos( ωt ) • Power enters on RHS and leaves through the damping term on the LHS • No power leaves/enters the oscillator through the ¨ x or x terms. • One way of looking at almost every oscillator is that it is just a mechanism for converting power from some driver to another dissipater (eg. gravitational energy from falling water drives turbines and this energy is, in turn, dissipated by the transformers generating current on the electrical grid). 3. Out-of-phase Oscillations • Recall that we have the particular solution X ( t ) = A ( ω ) cos( ωt- δ ) • The solution actually came in two pieces: G cos( ωt ) + H sin( ωt ) = A ( ω ) cos δ cos( ωt ) + A ( ω ) sin δ sin( ωt ) • We called the “G” piece the in-phase part of the solution – since it is in-phase with the driving force....
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