hw2solution - Homework 2 Solution 1 The response can be...

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Solution 1. The response can be plotted from the solutions of the equation of motion for different damping ratios: (I) Overdamped case: 1: x t 2 1 n x 0 0 2 n 2 1 e 1 t 2 1 n x 0 0 2 n 2 1 e 2 t where 1  n n 2 1 , 2  n n 2 1 (II) Critically damped case: 1: x t x 0 n x 0 0 t e nt (III) Underdamped case: 1: x t e  nt x 0 cos d t  n x 0 0 d sin d t ,w h e r e d n 1 2 The plots for different initial conditions are shown for 10 s: (a) Natural frequency n 2rad/s , x 0 1 mm, 0 5 mm/s. 0 1 2 3 4 5 6 7 8 9 10 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Time (s) displacement (mm) Free response - x0 = 1 mm, v0 = 5 mm/s z=3 z=1 z=0.5 z=0.1
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hw2solution - Homework 2 Solution 1 The response can be...

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