pset_3 - ACM 95/100b Problem Set 3 January 23, 2009 Due by...

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January 23, 2009 Due by 5:00PM on 1/30/2009 Please deposit your problem set in the slot in 303 Firestone or upload it via Moodle. In either case please keep a copy of your problem set. Please remember to include your section number and section instructor. Because the problems are a little longer this week there are only 4 and the point count varies. Collaboration is allowed on all problems but please write up the solutions yourself. Problem 1 (10 points) Solve the initial value problem y 00 + 2 y 0 + y = u ( t ) y (0) = 0 y 0 (0) = 1 where u ( t ) is the unit step function discussed in class: u ( t ) = ( 0 t < 1 1 t 1 using the Laplace transform. Problem 2 (15 points) Consider the differential-delay equation dy ( t ) dt = y ( t - 1) t > 0 , with a starting condition y = 1 - 1 < t < 0 (a) Show that a continuous solution for this equation is given by y ( t ) = 1 + t 0 < t < 1 , t 2 2 + 3 2 1 < t < 2 , . . . . . . 1
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This note was uploaded on 12/12/2009 for the course ACM 95b taught by Professor Nilesa.pierce during the Winter '09 term at Caltech.

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pset_3 - ACM 95/100b Problem Set 3 January 23, 2009 Due by...

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