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# HW0 - ECE 493 Univ of Illinois HW#0 Version 1.00 Due Thu...

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ECE 493 HW #0 – Version 1.00 January 19, 2011 Spring 2011 Univ. of Illinois Due Thu, Jan. 25 Prof. Allen Topic of this homework: Evaluation exercises; Not graded. Deliverables: You best attempt at the questions. If you don’t know, just say so. I’m looking for your collective baseline. It is not in your best interest to answer questions you don’t understand (e.g., don’t copy stuff from Wikipedia). 1. (a) Integrate the equation F = ma where F is the force, acceler- ation a = dv/dt is the rate of change of the velocity v ( t ), and m is the mass. Solution: F ( t ) = m dv dt it follows that integraldisplay dv = 1 m integraldisplay F ( t ) dt. Justify the above procedures and clean up the argument. (b) If F ( t ) = δ ( t ) then the velocity is a step function at t=0 v ( t ) = 1 m integraldisplay δ ( t ) /mdt = u ( t ) . (c) What is the displacement x ( t ) if v dx/dt ? (d) What if F ( t ) = sin( cx - t )? Find ∂F ∂x =? 2. Given the differential equation ¨ x + b ( x ) ˙ x + 1 = 0 (a) What is the order (b) If b ( x ) = 0, the equation homogeneous or inhomogeneous? Explain.

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HW0 - ECE 493 Univ of Illinois HW#0 Version 1.00 Due Thu...

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