HWK3514_HWK_8_solution_Fall_2007

HWK3514_HWK_8_solution_Fall_2007 - ME 3514 System Dynamics...

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ME3514 - HWK - Burdisso - 91 ME 3514 – System Dynamics HOMEWORK #8 - SOLUTION DUE: 11/7/07 1. Sketch the response of the following 1 st order system to a step input. () 5 2 () 2 1 (0 ) 0 dx t x t t and x dt + = Solution : To find the time constant T, the EOM is divided by 2 to give 5( ) () 1 2 dx t x t t and x dt + == Thus, the time constant is T=2.5 and the steady-state solution is 1 xt →∞ = . Then, 1 1 2.5 Tan T α NAME: 2.5 1 1 2.5 2.5 0.95
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ME3514 - HWK - Burdisso - 92 2. Sketch the response of the following 1 st order system to a ramp input with r =0.1. () 52 ( ) 2 ( 0 ) 0 dx t x t rt and x dt + = Solution To find the time constant T, the EOM is divided by 2 to give 5( ) () 0 .1 (0 ) 0 2 dx t x t t and x dt + == Thus, the time constant is T=2.5. Then, 0.1 t 0.1 0.25 T = 2.5 T =
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ME3514 - HWK - Burdisso - 93 3. Sketch the response of the following 2 nd order system to the initial conditions 2 2 () 10 5 200 ( ) 0 (0) 1 (0) 0 dxt d xt dt dt IC x x + += == ± Solution Need to compute natural frequency and damping ratio: 200 4.47 / 10 55 0.055 2 2 10 4.47 n n rad s m ω ξ = ×× Response is a exponentially decaying harmonic with frequency 2 1 0.055 ( 1.4 ) dn nn Ts ωω =− = 1.4 n = 0.25 n t t ee ξω =
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ME3514 - HWK - Burdisso - 94 4. Estimate: Initial conditions, natural frequency, damping ratio, and damped natural frequency.
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HWK3514_HWK_8_solution_Fall_2007 - ME 3514 System Dynamics...

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