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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).
- Fall '07