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105PS4 - large but the end points of the interval do of...

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UNIVERSITY OF CALIFORNIA AT BERKELEY DEPARTMENT OF PHYSICS PHYSICS 105 SPRING SEMESTER 2009 LEROY T. KERTH Problem Set 4 Due February 23, 2009 1. Derive expressions similar to equations 7, 24 and 26 in the notes on the Harmonic Oscillator, for arbitrary initial conditions, i . e . at t = 0, x= x o and ! x = v 0 . Problems 2 through 6 are from Taylor: 2 5.2 Page207 3 5.4 Page 207 4. 5.18 Page 209 5. 5.22 Page 209 6. 5.42 Page 212 7. An object is acted on by a linear restoring force, there is no damping. Determine the time the object spends in an interval between x and x + Îx, where Îx may be
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Unformatted text preview: large, but the end points of the interval do, of course fall within the limits of the oscillation ± x o . Express the time as a fraction of the period. Examine the limiting case of Îxü x o . Sketch the fraction as a function of x for fixed Îx. Give a qualitative explanation of the trend. 8. A cylinder of height h and density ® floats vertically in a liquid of density ®. Find the net force on the cylinder as a function of its displacement from equilibrium. Suppose the cylinder is poked so that it bobs up and down. Find the frequency of the oscillation....
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