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MEM423Su07-08_Ex1_soln_stud

# MEM423Su07-08_Ex1_soln_stud - MEM 423 Mechanics of...

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MEM 423: Mechanics of Vibrations _______________________________________________________________________ Mid-term Examination I Summer 2007-08 Allotted time: 1hr. 30 min. _______________________________________________________________________ Problem I: (50%) The model for this double pendulum is given below – you do not need to derive this. Using that model determine the natural frequencies and the associated modal vectors for the case 1 2 1 2 , and . m m m l l l = = = = A P

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2 1 2 1 1 1 2 1 2 1 2 1 2 2 2 2 2 1 2 2 2 2 ( ) 0 ( ) 0 0 m m gl m m l m l l m gl m l l m l θ θ θ θ + +   + =       && &&
Problem 2: (50%) For the pulley system shown below, (the pulley rotates about the fixed pivot and the mass moves left and right. There is no vertical motion of the pulley and the mass. The only ‘elastic/spring medium’ is ‘k’)) a. determine the number of degrees of freedom. b. develop an equivalent system with respect to the coordinate x shown. If you are using energy approach to obtain equivalent damper, then use the expression for energy in a damper as 0.5*(damping-coefficient,c)*(its velocity-squared).

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MEM423Su07-08_Ex1_soln_stud - MEM 423 Mechanics of...

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