263ps06 - a phase angle of t = / 2. Show that in the...

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Physics 263: Problem Set #6 These problems are due at the end of the day on Tuesday, May 10. 1. Morin 11.60 (Passing trains) p. 563 2. Morin 12.29 (Decay in to photons) p. 617 3. Morin 4.19 (Removing a spring) p. 123 4. Morin 4.28 (Ratio of maxima) p. 125 5. Morin 4.30 (No damping force) p. 126 6. Damped oscillators are often characterized by the dimensionless “quality factor” Q ˜ ω 2 γ where ˜ ω ω 2 - γ 2 ω for light damping (i.e. large Q ). In the absence of damping, the oscillator coordinate obeys x ( t ) = x 0 sin( ωt ), and the maximum displacement occurs exactly half-way between zero-crossing, i.e. a quarter of the way through the motion at
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Unformatted text preview: a phase angle of t = / 2. Show that in the presence of (light) damping, the maximum occurs at phase angle / 2-1 2 Q . (This observation is useful when using an oscilloscope, which is good at nding zero-crossings and peaks.) 7. Show that for a lightly damped oscillator the energy lost each cycle is a fraction 2 /Q of the total energy stored in the oscillator. 8. (BONUS) Morin 4.22 (Projectile on a spring) 9. Shankar, problem 5.4.3 pg. 103. 10. Shankar, problem 5.4.4 pg. 103. 11. Shankar, problem 5.4.5 pg. 103....
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