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Unformatted text preview: MATHEMATICS 201, SECTION A01
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Jubr6,2011 Name: Student Number: Duration: 50 min. Maximum score: 30.
The test has 5 problems and 5 pages. '
Full answers, please. Justify your statements. The Sharp EL—510R scientiﬁc calculator is the only calculator allowed. No other aids
suchas books, notes or formula sheets are permitted. 1. Find a fundamental set of solutions to the differential equation 3/" — Zay’ + (a2 + b2)y = 0. ; 2.
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L P ‘ gt, Midterm 2, July 2011 _ 3. MATH 201 (a) Find the general solution of the homogeneous equation 4
my" — 3y’ + Ey = 0. Hint: You can rewrite this equation as a Cauchy—Euler equation. Page 3 . fl
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f l 7k. f R + X / Midterm 2, July 2011 MATH 201 Page 4 4. A body With mass of 0.5 kg is attached to the end of a spring which stretches 2 m with a force of 8 N. The surrounding medium imposes a damping force equal to twice the
velocity. (a) Find k, the spring constant. 141‘ ii: 1—” i» , :> s lql) "*3 i V, I. kiss (b) When the mass reaches equilibrium and has no instantaneous velocity, its sup—
port begins to oscillate vertically according to f (t) = 20 cos(t). Determine the
differential equation of motion With its appropriate initial conditions. W] I: / r _ .. .
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"XLORG w/[olsd (c) The equation of motion associated with this system is + @ cos(t) + j—Zsin(t) 56 72
) 13 13 — —— cos(2t) — 1—3 sin(2t) x(t) = 6—2t( 13 Identify the transient term (solution) and the steady—state term (solution). , l , r i A  (1
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5‘ i3» ’ Aka .9611 Midterm 2, July 2011 V MATH 201 Page 6 [5] 5. Find a family of solutions for the given differential equation. Also, ﬁnd a singular
solution. No marks will be given for guessing the singular solution; you must provide a
solid piece of evidence that leads you directly to conclude that it is a singular solution. 1 (y ~_ 2)y// _ §(yl)2 : 0 dis/2 0!?“ C/h Ci
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