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315 Midterm - NORTH CAROLINA STATE UNIVERSITY Department of...

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Unformatted text preview: NORTH CAROLINA STATE UNIVERSITY Department of Mechanical and Aerospace Engineering MAE 315-1 Dynamics of Machines Summer I, 2010 MID-TERM EXAMINATION (June 9, 2010) Name Student ID Problem 15 20 15 —— INSTRUCTIONS: 1. This is a closed book exam. You are allowed to have 9113; help sheet of hand—written summary. 2. Explicitly state What you are solving for and how. Box your final answers. Also, one word answers are not acceptable. 3. Be neat and clear. Your exams must be stapled. Name Problem 1 (15 points) A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves. The natural period of this system is 0.55ec. If an identical spring is cut so that one part is one- fourth and the other part three-fourths of the original length, and the same mass is connected to the two parts, write out the equation of motion for both cases and determine the natural period of the second system. I I 7 3 V 'fi‘ ¥ \ km km (a) (b) Hint: The stiffness of the spring is inversely proportional to its length. 9&6“; Tb: ‘fmfs .1. 7339. too :4 (1,) M4 fowluldwwuihl. In pray and. cfdl‘lj Wo-ol‘ 9A 2K. 1“ P3,“), #4 74+]: CWW «42 4k M 555.4 ”22¢;qu 7mfm) #4 jwMMj “M 7"”0’“ c“ 3” m5€+c2k+1k)3‘:° b.5130: zit/T7“ =o.1’9u. :2/1;=r'n~. In W (5), W5 3W0/rrvlj 20/14 M KR . m '- Ta = 75‘ : 217 m “5 ‘11-th : ENE =EMJ‘ : 0.435 (your). Name Problem 2 (20 points) Given the following mechanism with m = 4kg, 6 = 2m, 0 = SON/msec, k = 200N / m. 1. Derive its equation of motion in terms of rotation angle 0, 2. Determine the natural frequency and damping ratio of the mechanism, 3. For the initial condition 0(0) = 0.1md, 9(0) = —0.2rad/ sec, determine its solution. govt“: I, W100” Java) FED 6f 1*: 5M". Tb» My 96w“ 2/”, :: ox ‘ W£M& Hie €296 G“ r x2 1-1 s 5 " t 99‘ ‘ kjez~0:e+“‘?!fl~;€=‘-Jo0 0 u 2. m I. — 75mg +( f“ — jig-“41‘ 71».qu w EoMCA T z~ 2‘ 3’ fi“36+%fi+i§i6:° 75W” 7’“ “J 057'”; rad-lo £4 7i : 45,5 __ 3c _ 2X27Tmlk‘xw.‘ _ ‘4'“a’w ~ 0"” <1 ' A6”) 9L4 atom/444 W4 franémj :4 004 : l-led.‘ ‘: lfJ‘ll'G‘fJ/q“ 3, gag T<|, «A wL-Hn fem wot/(Li 60*): @4'3'Wxamuf‘) F 7; ‘ 1‘3 0‘) =’- *fw-‘(E Qi‘w‘bugCWdt +14) [email protected]~rw‘*w4 Cadmf’rf) "' 1”“ TN“ ”Mao/l M‘fiw, ma LA 9(0) : 0.1 : @Q, 006): 0, too, .9‘2'67’4’)‘ 6C0) 1“- -o.z :: -j‘[email protected] a”? + MLQ Q 944419-81” “32.3) . 7‘ <3"— @ZO./Do/H4) {oz/r22“ Name Problem 3 (15 points) Consider the base excitation problem for the following configuration. Support 1 x(t) I C 1m) = Ysin W The base motion is a displacement transmitted through a dashdot or pure damping element. Derive its equation of motion, the steady—state motion, and the force transmitted to the support in steady state. gab“: W42 ohm 7.3.3 f” M M, “A m N‘BW‘W/s 3N4 LN kx MEX‘: :Fx: ‘kX“Q(‘>l-j) -\ \ ‘ Mlnzr+0m+kx=c 2.va _ c(&_‘j) j " fo‘b (wbt) ...
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