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Unformatted text preview: torque = d dt (angular momentum) `mg sin = d dt m` 2 d dt `mg sin = m` 2 d 2 dt 2 d 2 dt 2 + g ` sin = 0 . 9. According to Problem 8, with ` = g , the function ( t ) satises the identity ( ) 2 2 cos = C = const . (4.9) Our rst purpose is to determine the constant C . Let t a denote the moment when pendulum is in the apex point, i.e., ( t a ) = . Since it doesnt cross the apex over, we also have ( t a ) = 0. Substituting these two values into (4.9), we obtain 2 2 cos = C C = 1 . 229...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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