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# 3 - MA’241 Test 3 Fall 2007 Form A Your name on your test...

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Unformatted text preview: MA’241 Test 3 Fall 2007 Form A Your name on your test is your pledge that you will not give nor receive information/help on this test. ' No calculators, No cell phones, No PDAs Show all work. Circle your ﬁnal answer. No credit for guessing. Please begin each problem on a clean page in the blue book. Please do not leave if you have to pass over a peer on your row. 1. (15 pts) Solve the 2nd order differential equation with the given initial values y"+ 2y' + 2y = o y(0) = o, y'(0) a 10 2.- (15 pts) The complementary solution for y" + 3}” + 2y = x2 is yc = Clea" + Cze" Use the method of undetermined coefﬁcients to ﬁnd the particular solution, yp. 3. Determine if the sequence converges or diverges. Show all steps. 4. Determine if the series converges or diverges. Name the test, show the criteria for the test and make a concluding statement. If the series converges, ﬁnd the sum. (10 points each) 3 3 a. 3+—+...+ H 4 4 11:14,; +1) =2(?1{_Z+—1) n-l c 2 3n2 ' 2 ".1” +1 Continue on next page +... Form A continued: 5. (10 points)A bacterial culture with growth constant 0.05 initially contains 5th cells and grows at a rate proportional to its size. Let P(t) be the number of cells in t hours Find the rate of growth when the population 15 10, 000 cells Include units. 6. (10 points) Let x(t) be the position of the mass (with respect to equilibrium) on the end of a spring at any time t. A spring with mass 1 kg has damping constant 6 and spring constant 9. Determine if this spring is over damping, critical . damping, or under damping. X3: X %” ,Lf 3333M ex g) _ 520° :32 ex :0 V? is M W1 m (”if 017W” 3M4 m a M) I’) ,’———— ; C" j‘ Y” W W HF/r W3 ﬁ;awdnu0 (/7! “34 6 57"” Low 6 mice (WW my /‘ UL 1/ VWv jww “909 hi}? “KW U Kama” ;OM3 /:%F %1 ﬂ 1‘" 9° ”33a I W (MW ...
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3 - MA’241 Test 3 Fall 2007 Form A Your name on your test...

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