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Linearize the differential equation by assuming that θ is small. (The resuit is called the small angle approximation.) F
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Linearize the differential equation by assuming that θ is small. (The resuit is called the small angle approximation.) F
Linearize the differential equation by assuming that θ is small. (The resuit is called the small angle approximation.) For small θ it can be assumed that the vertical acceleration of the ball is negligible. This latter assumption enables you to determine the (constant) value of the vertical reaction force that is exerted by the cart on the rod. Assume a proportional-derivative (PD) control scheme (Le., no integral component)Substitute the expression for a PD control scheme for F(t) in the differential equation derived under Task 2 . Then write the differential equation with all terms placed on the lefthand side. (That is, the righthand side should be zero.)
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