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# exam2W09sol - Name Section/Time of lecture Professor GSI...

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Name: -------------------------------- Section/Time of lecture: -------------------------------- Professor/ GSI: ----------------------------- ? i~ MATH 216 WINTER 2009 MIDTERM II To get full score you need to carefully explain what you did. No calculators allowed. 1

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I Problem I Points I Score I 1 7 2 20 3 20 4 20 5 15 + 2 2 I TOTAL I 84 2
Problem 1. a-(5pt): A mass of lkg is attached to the end of a spring that is streched 25cm by force lN. It is set in motion with an initial position x 0 = 0 and initial velocity v 0 = 10m/ s. Set up BUT DO NOT SOLVE the initial value problem describing the spring system. ~ = I N ::: ~k 5 f v1 r:5 CfY\S~Ct() i I k-- .2S" m></"-+ kx =0 \~~ -t- lf_x: ___ Q ___ ___,! / x r D} == 9 x/ 1 o) -:::. I 0 b-(2pt): Assume that x(t) = 2 sin(t) + 3 cos(t) describes the motion of a free undamped spring system. Find the amplitude of the motion. A~L B=3 ------~ C .::: ~ 2 J.. --t :>L. 3

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Problem 2. a-(4pt): Set up BUT DO NOT SOLVE for the appropriate particular solution for the equation y" + 4y = x cos(2x) + ex using the Method of Undetermined Coefficients. b-(6pt): Find a particular solution for y"- y'- 2y = cos(x) j r :::: AU::J/( -t j3 ~r- j / :: - )-\s~ It\ X -,.- 13 Lb.J X Jt- ~- A (AY.)~ - B ~x: l- A~x -13~x} [-A~><-r l3u-J><J -2[ A(.frJK --t- D~l(J =o (4:1)c -A-8~2A= f------=; -3A--'E>~I ~ ~ 3.B - B + A - 2l3> -:::: o =---7 p ~-~, A:-u
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exam2W09sol - Name Section/Time of lecture Professor GSI...

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