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# HWCE_1 - F applied horizontally to the right at the point...

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Assignment for HW/CE#1, due Wednesday, Feb 3. 1. Consider a pendulum system as shown below. Assume the angle θ is small so that sin( θ) ~ θ . Assume that the length of the massless rod is l meters from the pivot point to the center of the mass m in kg. The force F may be assumed to be perfectly horizontal and constitutes an input to the system. Assume that the pivot point introduces friction modeled by a linear relationship with friction constant b. θ F m a) Find matrices F, G, H, and scalar J for a state variable description of the system where θ ϖ θ = = = y F u and x b) Find a transfer function G(s) relating the output y to the input F , i.e. ) ( ) ( ) ( s F s s G θ =

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2. Work problem 2.1, part a, on page 62 of Franklin’s text but assume a force
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Unformatted text preview: F applied horizontally to the right at the point where the output y is taken. Put your equations in state variable form, that is, find matrices F, G, H, and scalar J for a state variable description of the system where y F u v v x x as taken is output the and 2 1 2 1 = = x 3. Find f(t) using partial fraction expansions for each of the following Laplace transforms 9 1 ) ( c) ) 68 4 ( ) 6 ( 8 ) ( b) ) 12 7 ( 10 ) ( a) 2 2 2 + = + + + = + + = s s F s s s s s F s s s s F 4. Work problem 3.19b on page 153 in Franklin’s text....
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HWCE_1 - F applied horizontally to the right at the point...

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