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midterm1

# midterm1 - 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 Spring Semester, 2008 MID-TERM EXAMINATION #1 (Feb. 29, 2008) Name Student ID INSTRUCTIONS: 1. This is a closed book exam. You are allowed to have one 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 (10 points) The airplane’s steering-gear mechanism for the nose wheel of its landing gear can be modeled as a single degree of freedom system, where k1 is a torsional spring and k2 is a linear spring constant. Use energy method to derive the equation of motion and natural frequency of the mechanism. (Steering wheel) / (Tire—wheel Ill] ‘ M assembly) —_ QM; 71a «cowl Iowa. W33 “A T: “EMiﬁ‘tJi’aél Nofztlwt- aizré/ 19L” T= ‘Lri’+i}(—°‘r)2 =icm+iw J. y‘- V: {:kz’xz'l'i—klez v: 4; klxztdgk.(—:)2:~i(kx+-%)O(z. todvl :4 Inwvul, N» T+V:c' %(T+V):o a \ J t -- (M+?)'X’X + Clu‘l~ 13;)Ixyzo => (tn-{3) «3? + (kink ‘51)“:0 ‘EO/M. *3. TM frnﬁuMCj :A Name Problem 2 (20 points) Given a mass-spring system on an inclined plane. I'r. av 4' N we a 1. If the position of mass is deﬁned from its equilibrium position and points downwards along the plane, derive its equation of motion. 2. Given m = 1kg, k1 = k2 = 2N/m, Solve the free response for 22(0) = 0.01m and = Om/s. garb/«1 1- we JYW F732) W M NWR-n/s new bag, m 7‘” \ Moi: Zsz—km—knc M;+(I<‘Tkz)9(:o 2. For v/q 3:1’34 EOM, U4 fun erM {A «a, 1': A (3,. (code) + 73 goon) W ‘ kl‘l‘k “’“~ M ‘ : 2 (MAJ/s) Gsm uh M4 bow-(Jim xCo):ovoi '9 Mo)?- Om/S» M Ma {0-01': A~i+ [3.0 ° : ~¢4wmo + Ban-I .‘- Azo‘o/ B:°\ Theft/R «0H: °~°’I QSCZ“) Cm) Name Problem 3 (20 points) Consider the damped pendulum mechanism pivoted at point 0, which can be used to model a brake pedal in automobile. Assume that mass of the rod is negligible, and rotational angle is small. Given m = 40kg, k = 4 X 103N/m,c = 200Ns/m and the harmonic force F(t) = 10 cos(10t)N. 1. Derive the equation of motion in terms of rotational angle 0, 2. Calculate undamped and damped natural frequencies, 3. Solve the steady-state motion caused by harmonic forcing. Q04“: ‘~ Fin-9+ we clam T33) ‘DLM ‘ff’lj 146‘ = 2M0 _ M‘é‘ = «es-10. —- ant-oi + PM “916‘ 4- (>922?) “McKee =1o4’ c.5001“) 250/14 90 v/«x DL‘m/NIJ W 34 “M 2 Want 2 4.948(M/s) 3. Din-0‘14- mmgg “My” VL‘ Vega on“ MM \‘A ‘3“)[email protected]:+~f) - . 2'. .0 C J“- £62)z_H2I%)x i? ) w 53 :m“(—zl—L) 1: ~O.3i(Cv~mi) 60*) = «MBIZ‘CW (¢o++o.3/() (ml) ...
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