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MIT16_07F09_hw09

# MIT16_07F09_hw09 - NAME Massachusetts Institute of...

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Unformatted text preview: NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 9 Out date: Oct 31, 2007 Due date: Nov. 7, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Study Time Turn in each problem on separate sheets so that grading can be done in parallel Problem 1 (10 points) The displacement h of an elastic beam under the action of a point load P is given by PL 3 h = (1) 3 EI where L is the length; EI is the product of Young’s modulus and the cross-sectional area moment of the beam I. Consider case a): a beam with a mass m at its tip. a-1) Take the beam as massless; ignore gravity; write Newton’s law for the motion of the mass x ( t ). a-2) What is the natural frequency of oscillation of the beam-mass system? Now consider case b): two beams of different stiffnesses EI 1 and EI 2 are joined by a spring of stiffness k which exerts a force proportional to its change in length. Put an equal mass m at the end of each beam. Ignore gravity....
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MIT16_07F09_hw09 - NAME Massachusetts Institute of...

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