Homework2_2010

Homework2_2010 - ME580 Nonlinear Systems Home work #2 Due:...

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ME580 Nonlinear Systems Due: Sept. 23, 2010 Home work #2 1. The velocity v ( t ) of a skydiver falling to the ground is governed by 2 mv mg kv , where m is the mass of the skydiver, g is the acceleration due to gravity, and k 0 is a constant related to the air resistance the diver faces. a) Find the analytical solution for the skydiver's velocity v ( t ) as a function of time, assuming that the initial velocity is v (0) 0. b) Find the limiting value of v ( t ) as t . (Strogatz: Nonlinear Dynamics and Chaos; pp. 38) 2. Consider the model chemical reaction A X 2 X , in which one molecule of X combines with another molecule of A to form two molecules of X. This implies that the chemical X stimulates its own production, a process called autocatalysis. This positive feedback process results in a chain reaction that eventually is limited by a "back reaction" in which 2X returns to A+X. According to the law of mass action , the rate of an elementary reaction is proportional to the product of the concentrations of the reactants. Let x and a
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Homework2_2010 - ME580 Nonlinear Systems Home work #2 Due:...

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