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hw1_spring_09

# hw1_spring_09 - EML 6267 Assignment#1 Spring 2009 Please...

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EML 6267 Assignment #1 Spring 2009 Please remember to put your name on your assignment. Due: 1/21/09 1. (25 pts.) For a given single degree-of-freedom (SDOF) lumped parameter system (undamped), the free vibration, x ( t ), is shown below. a) (20 pts.) If the motion was initiated with a velocity of 2 π mm/s and zero initial displacement, express the motion in the forms show below (use units of mm): i) (5 pts.) x ( t ) = A cos( ω n t ) + B sin( ω n t ) ii) (5 pts.) x ( t ) = C cos( ω n t + Φ c ) iii) (5 pts.) x ( t ) = C sin( ω n t + Φ s ) iv) (5 pts.) x ( t ) = De Ee i t i t n n ( ) ( ) ω ω + . b) (5 pts.) Given your expression for x ( t ) in part a-i), write an expression for the velocity, dx ( t )/ dt , (mm/s). Plot your result over the same time interval (0 to 0.5 s) shown above. Verify that the peak velocity is ω n B . Please include the computer code used to generate the plot. 2. (20 pts.) For a SDOF lumped parameter system under free vibration with the following values for the mass, stiffness and damping: m = 1.0 kg 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Time (s) x (mm) HW 1, problem 1

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c = 10.0 N-s/m k = 4.0e4 N/m a) (5 pts.) Find
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hw1_spring_09 - EML 6267 Assignment#1 Spring 2009 Please...

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