AE383HW5 - find its impulse response. Show that this...

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AE 383 System Dynamics Homework 5 Handed out: July 20, 2006 Due: July 25, 2006 1. A free vibration of the system shown in the Figure indicates that the amplitude of vibration decreases to 25% of the value at t = t 0 after four cycles of motion. Determine the viscous friction coefficient b of the system if m = 1kg and k = 500N/m. 2. Impulse response of a system is given as h(t) = sin( ω t). Find the response of this system to a unit step input using a) Laplace trasform. b) Convolution integral 3. Consider the second order system in its standard form ) ( 1 2 2 t f x x n n = + + ω ς Assume that the system is underdamped,
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Unformatted text preview: find its impulse response. Show that this impulse response is identical with the response to a suitably chosen initial velocity. 4. Consider the dynamical systems represented by the following transfer functions. Plot the poles of each system on the complex pane and determine whether they are stable or not. 5 1 ) ( 1 + = s s G 5 10 ) ( 2-= s s G 5 4 1 ) ( 2 3 + + = s s s G 5 4 1 ) ( 2 4 +-= s s s G ) 6 8 )( 5 3 ( 1 ) ( 2 2 5 + + + + = s s s s s G 100 200 300 400 500 600 700 800 900-0.8-0.6-0.4-0.2 0.2 0.4 0.6 0.8 1 X0 X4=0.25*X0 t0...
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