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lec18 - Lecture 18 P112 Agenda for today Challenge friction...

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Lecture 18 P112 Feb 28, 2008
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Agenda for today Challenge topic: Projectile motion with friction How, in practice, to solve differential equations NOT ON ANY EXAMS – (Maybe a homework question)
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Differential Equations An equation in which derivatives of a function appear as variables They will cross your path often! e.g.Oscillations,… Example: Population growth: the number of bunny’s born each year is proportional to the number of mommy bunnies b is a constant. Problem: derive an expression for N dN dt = bN ( t )
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solving differential equations by “Separation of Variables” Population Growth: dN ( t ) dt = bN ( t ) 1 N dN dt dt = bdt 1 N dN dt dt = bdt dN N N i N f = b dt t i t f log( N f N i ) = b ( t f t i ) N f = N i e b ( t f t i )
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Harder Differential equation Projectile motion -- with air resistance Break into components: No “analytic” solution
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Dimensional Analysis Terminal velocity From m,g, and D, how do you make a velocity?
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