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An object of mass m moves in a circular orbital under the influence of an harmonic oscillator potential U(r)=1/2(alpha)r^2 where alpha is constant and r is measured from the center of the circle. Since the center of circular orbit and the force center coincide, the force must always be directed radially inward toward the center of the circle. Use this fact to show that the orbital period is independent of the radius of the orbit.
Determine the energy of the orbiting object and its angular momentum as functions of the orbital radius r.
A 90 uF capacitor and a 15m H inductor are in series with a 185 O resistor, What is the resonant frequency
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Their motions have equal periods, but the radius of skater A's circle is half that of skater B's circle. Evaluate the ratio of the magnitudes of the forces acting on each skater?
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A sealed tank containing seawater to a height of 11.1 also contains air above the water at a gauge pressure of 2.95. Water flows out from the bottom through a small hole.
Starting from rest, an elevator has a constant acceleration of 0.621 m/s2 for a period of 6.25 sec., find the displacement of the elevator
A block is attached to a ceiling by a spring of force constant k. When pulled down and released, what is the force constant k of the spring
Write the expression of the force fl j corresponding to the Uu potential energy term. Derive the expression of the distance r m i n at which Uu has its minimum value, as a function of the parameters a and/or E.
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