286practicefinal - 286-E1, Spring 2010Practice Final...

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Unformatted text preview: 286-E1, Spring 2010Practice Final Exam11. (a) (10 pts) Find allaRso that the solution of the initial value problemx=x4-1, x(0) =asatisfies limtx(t) =-1.(b) (10 pts) Classify the type of origin as a critical point of the system:ddt~x=-kk~xwherek6= 0 is an arbitrary nonzero real number. Describe geometrically the trajectories ofthis system.2. (15 pts) Find the general solution of the equation:(x2+ 1)dydx+xy=x3. (20 pts) Find the general solution of the equation:(2xsinycosy)y= 4x2+ sin2y4. (10 pts) Compute the Fourier series of the 4-periodic extension of the function:f(t) =,t22,-2t <5. Suppose that a massm= 2kgis attached to a spring with spring constantk= 32N/mwhose otherend is fixed to a wall.(a) (10 pts) Find the value of damping coefficientcfor which this system is critically damped.What is the general solution for the position functionx(t) of the mass at timetin this case?...
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This note was uploaded on 08/25/2010 for the course MATH 286 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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286practicefinal - 286-E1, Spring 2010Practice Final...

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