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... must be satisfied. Because r0 6= 0, this quadratic equation determines for s two values, which in special case may coincide. The first of the equations (6) leaves a0 (6= 0) arbitrary. The next linear equations in an allow to solve successively the constants a1 , a2 , . . . provided that the first co ...
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Adiabatic Theorem

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... Functions f x   3x  1 and g x   x 2  7 are defined on the set of real numbers. a) Find h x  where h x   g f x  . b) i) Write down the coordinates of the minimum turning point of y  h x . ii) Hence state the range of the function h. Differentiate 1 2 sin x 4 with respect to x. ...
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Homogeneous Equations with Constant Coefficients

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... Part II consists of six relatively short problems, worth ten points each. The short problems can be worked out on the front page of the sheet provided, but use the back if you need more room. In any case please be neat! Also, two extra pages are provided at the back. Use these if you need to, but be ...
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... If the forces can be resolved directly from the free-body diagram (often the case in 2-D problems), use the scalar form of the equation of motion. In more complex cases (usually 3-D), a Cartesian vector is written for every force and a vector analysis is often best. A Cartesian vector formulation of ...
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Routhian mechanics

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