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Unformatted text preview: 2 k x ϖ = , then we have the differential equation 2 2 2 2 2 d x k d x x x dt m dt + = + = . Ex3. Simple Pendulum ***The picture is on page 14*** Again, the displacement s is a function of time and 2 2 2 2 d s d s l a l dt dt θ = = = . From the Newton’s 2 nd law, we have ( 29 ( 29 2 2 2 2 sin sin 0. d d g F ma m l mg dt dt l = = = + = When is small, ( 29 sin . So, the above ODE can changed to ( 29 2 2 2 2 sin d g d g dt l dt l + = + = . Ex4. Charge on a Capacitor...
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 Fall '06
 EDeSturler
 Math, Calculus, Equations, Force, Robert Hooke

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