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**Unformatted text preview: **E x U = ) ( , where x are the extreme points of the motion. Rather than solve a quadratic, note that k F k F x k 2 2 2 1 ) (--, so E x U = ) ( becomes , 2 2 1 2 2 k F k F x k F k F k F x k =-=- - . 3 k F x k F x-= =-+ f) The maximum kinetic energy occurs when ) ( x U is a minimum, the point k F x = found in part (b). At this point k F k F k F U E K 2 2 2 2 ) ( ) ( =--=-= , so mk F v 2 = ....

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