# ps12 - A hollow spherical ball of mass m and of radius r is...

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Assignment 12, Phys1112 Spring 2010 Due April 26 Problem 5 A mass m =1 kg on a spring (with no damping) has a period of 2 sec. At time t = 0, the mass is at x =1 / 3 m and has velocity v =1 / 2 m/s in the positive x direction. (a) What is the position x ( t ) for subsequent times t ? (b) If you did not use energy ideas in part (a), verify that the amplitude is consistent with the total energy. Problem 6 A pendulum is constructed out of a rod of length L , by passing an axle through it a distance L/ 4 from the top. What is the period of the oscillations? Problem 7 A particle of mass m experiences a force due to a potential energy U = U 0 cos( x/± ), where U 0 and ± are constants. The particle has a maximum kinetic energy that is much less than U 0 and is oscillating back and forth in a stable minimum of the potential. What is the period of these oscillations? Problem 8

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Unformatted text preview: A hollow spherical ball of mass m and of radius r is rolling back and forth in the bottom of a bowl in the shape of a hemisphere of radius R . You can assume that r R . (a) Write an expression for the total energy E of the ball as function of , the distance of the ball from the bottom of the bowl as measured along the bowl, and v the speed of the ball. (b) What is an approximate expression for E when is very small? (c) By comparing with the total energy E for a mass on a spring, calculate the period of this motion. Check the units of your nal answer. Problem 9 1 By plugging into the diferential equation For a damped mass on a spring, m d 2 x dt 2 =-kx-b dx dt veriFy the solution: x ( t ) = A e-bt/ 2 m cos( t + ) where = k/m-b 2 / 4 m 2 . 2...
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## This note was uploaded on 08/04/2011 for the course PHYS 1112 taught by Professor Leclair,a during the Fall '07 term at Cornell University (Engineering School).

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ps12 - A hollow spherical ball of mass m and of radius r is...

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