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

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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 ± ²³´µ¶ . 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 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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This note was uploaded on 12/28/2011 for the course PHYSICS 273 taught by Professor Monroec during the Fall '11 term at Maryland.

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