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# HW1 - The total height is L Assume no damping At time t = 0...

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Phys 273 Homework #1 due Sept 7, 2010 1-7. A thin circular hoop of radius a is hung over a sharp horizontal knife edge. Show that the hoop oscillates with an oscillation frequency . 1-8. A marble thrown into a bowl executes oscillatory motion. Assuming that the inner surface of the bowl is parabolic ( y = ax 2 ) and the marble has a mass m , find the oscillation frequency. Neglect friction and you can assume small oscillation amplitude. 1-11. A capacitor of 5 F charged to 1 kV is discharged through an inductor of 2 H. The total resistance in the circuit is 5 m . (a) Is this a weakly damped RLC circuit? (b) Find the time by which one-half the initial energy stored in the capacitor has been dissipated. The time is measured from the instant when discharge is started. 3-4. A cylinder of diameter d floats with l of its length submerged.
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Unformatted text preview: The total height is L . Assume no damping. At time t = 0, the cylinder is pushed down a distance B and released. (a) What is the frequency of oscillation? (b) Draw a graph of velocity versus time from t = 0 to t = one period. The correct amplitude and phase should be included. 3-14. An object of mass 0.2 kg is hung from a spring whose spring constant is 80 N/m. The object is subject to a resistive force given by bv , where v is its velocity in meters per second. (a) Set up the differential equation of motion for free oscillations of the system. (b) If the damped frequency is ·¸ ´µ of the undamped frequency (when b = 0), what is the value of the constant b ? (c) What is the Q of the system, and by what factor is the amplitude of the oscillation reduced after 10 complete cycles?...
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