課程名稱︰機器動力學
課程性質︰選修
課程教師︰傅增隸
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰2008/4/23
考試時限（分鐘）：60
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.In figure 1, the block m1 is caused to oscillate by the attached pendulum
with length l and restrained by two equal linear springs k. The overall
friction between the block and its guideway is proportional to the relative
velocity squared, and the proportionality constant is B.
The moment of inertia of m2 about g2 is Ig.
(a) Identify clearly the generalized coordinate(s) on the graph. (6%)
(b) Formulate velocity of m2 and the kinetic energy of the system. (16%)
(c) Formulate the potential energy of the system. (7%)
(d) Determine the generalized force(s) on the system. (6%)
(e) Using Lagrange methods, obtain the differential equations of motion. (20%)
圖見課本4-9
2.In a dive maneuver, a jet airplane travels in a circular arc lying in a
vertical plane,which has a radius R of 1800 m as shown in figure 2.
The speed of the airplane is 950 km/h. The engine rotor rotates at 12,000
rpm clockwise when viewed from the tail of the airplane, and its moment of
inertia about the spin axis is 4.0 N-m-s2.
(a) Using the xyz coordinates shown in the figure, calculate the magnitude
and direction of the moment required for the airplane to make the turn. (20%)
(b) Will the head of airplane tilt left or right, and why?
(Answer without reasons is not acceptable, 10%)
(c) If the engine is subject to a moment of My = + 800 N-m, please determine
the direction and radius of the turn it can make. (15%)
圖略 本題有附公式
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