assign72k6

assign72k6 - The object is initially held at rest in a...

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Physics 153 Assignment 7 Due Friday November 3, 2006 by 5:30pm 1. A 3-kg object attached to a horizontal spring oscillates with amplitude A = 10 cm and frequency f = 2 Hz . (a) What is the force constant of the spring? (b) What is the period of oscillation? (c) What is the maximum speed of the object? (d) What is the maximum acceleration? 2. A particle moves in a circle of radius 40 cm with a constant speed of 80 cm/s . Find (a) the frequency and (b) the period of the motion. (c) Write an equation for the x-component of the position of the particle as a function of time t , assuming that the particle is on the x-axis at a time t = 0. 3. A body oscillates with simple harmonic motion according to the equation: x = (6 . 0 m ) cos[(3 π rad/s ) t + π/ 3 rad ] . What are (a) the displacement, (b) the velocity, (c) the acceleration, and (d) the phase at time t = 2 . 0 s ? Find also (c) the frequency and (f) the period of oscillation. 4. A massless spring hangs from the ceiling with a small object attached to its lower end.
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Unformatted text preview: The object is initially held at rest in a position y 1 such that the spring is not stretched. The object is then released from y 1 and oscillates up and down, with the lowest position being 10 cm below y 1 . (a) What is the frequency of the oscillation? (b) What is the speed of the object when it is 8 . cm below the initial position? (c) An object of mass300 g is attached to the ﬁrst object, after which the system oscillates with half of the original frequency. What is the mass of the ﬁrst object? (d) Relative to y 1 , where is the new equilibrium position with both objects attached to the spring? 5. A 500 g cylinder of base area a = 20 cm 2 and height h = 30 cm is ﬂoating upright in water. A 50 g mass, resting on top of the cylinder is suddenly removed. (a) Find the restoring force and show that the resulting motion is simple harmonic. (b) What are the amplitude and the period of the motion? 1...
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