Unformatted text preview: xpress your answer using the ratio
(d) At very low frequencies, how does this ratio compare with 1? At very high frequencies,
how does this ratio compare with 1? Do these results make sense?
10. Power in driven oscillations. A driven oscillator with mass m, spring constant k, and
damping coefficient b is driven by a force F0 cos ωt. The resulting steady-state
oscillations are described by x(t) = A cos (ωt + φ). The instantaneous power delivered to
the oscillator by the driving force is Pdrive(t) = F(t) v(t) (since F and v are colinear.)
(a) Show that the average power delivered by the driving force during one complete cycle is
1/2 ωF0 A sin(-φ).
(b) The instantaneous power dissipated by the damping force is Pdamp(t) = Fd v = -bv2. Show
that the average power dissipated during one cycle is -1/2 b ω2 A2.
(c) In steady state, your answers to (a) and (b) must be equal in magnitude; power in must
equal power dissipated so that the amplitude and mechanical energy of the oscillations
remains constant. Using your answer to (b), find the driving frequency at which the
average input power and the power dissipated by damping is a maximum. At this
maximum power, what is φ and what is the phase difference between the driving force
and the velocity? (The math is a bit messy here.)
Questions, Exercises and Problems from Y&F 12th Ed. for study and review: (Do not
turn these in!)
Volume 1, Chapter 13:
Questions: 1, 8, 12, 15, 20
Exercises: 4, 18, 30, 38, 39, 56, 57, 58, 60, 61
Problems: 63, 77, 103 Physics 2214, Spring 2011 5 Cornell University...
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This note was uploaded on 11/23/2012 for the course OR 350 at Cornell.