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HW13 - MAE 326 Spring 2008 HW 13 due Friday May 2 This...

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MAE 326 Spring 2008 HW 13, due Friday, May 2 This assignment will count as two HW grades. 1. B-9-11 2. B-9-13 3. B-11-2 Plot this graph using the Matlab bode function. Determine analytical expres- sions for the low and high frequency behavior of the frequency response. do this for amplitude and phase. Sketch the low and high frequency asymptotes on your plot and label them. 4. Consider the system whose sinusoidal transfer function has the Bode plot shown in figure 1. If the forcing input is u ( t ) = 3 sin( . 1 t ) + 2 cos(3 t + π/ 4), then what is the steady state output? Be careful about units, reading logarithmic scales and with dealing with the fact that one of the input signals already has a phase. -40 -30 -20 -10 0 10 20 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 -135 -90 -45 0 45 Phase (deg) Bode Diagram Frequency (rad/sec) Figure 1: Example Bode plot. 5. B-7-3 6. A simple model for an on-demand water heater is shown in figure 2. Water flows in from the top and is heated by the heating element before flowing out the bottom. We

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