Control ENG HW_Part_14

Control ENG HW_Part_14 - = t 325 ln 400 T From the data ,...

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- = T t 400 325 ln τ From the data , average of 9.647,11.2,9.788,10.9,9.87,9.95, and 9.75 is 10.16 sec. 5.7 Rewrite the sinusoidal response of first order system (eq 5.24) in terms of a cosine wave. Re express the forcing function equation (eq 5.19) as a cosine wave and compute the phase difference between input and output cosine waves. ω 1 1 ) ( 1 1 ) ( 2 2 + + = + = s s A s s s Y splitting into partial fractions then converting to laplace transforms ) sin( 1 1 ) ( 2 2 / 2 2 φ αωτ + + + + = - t A e A t Y t where φ = tan -1 ( ωτ ) As t →∝ ) - - + = + + = π 2 cos( 1 ) sin( 1 ) ( 2 2 2 2 t A t A s t Y - = + = t A t A t Y 2 cos ) sin( ) ( - = 2 cos ) ( t A t Y The phase difference = = - - - 2 2
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5.8 The mercury thermometer of problem 5.6 is allowed to come to equilibrium in the room temp at 75 deg F.Then it is immersed in a oil bath for a length of time less than 1 sec and quickly removed from the bath and re exposed to 75 deg F ambient condition. It may be estimated that the heat transfer coefficient to the thermometer in air is 1/ 5 th that in oil
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This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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Control ENG HW_Part_14 - = t 325 ln 400 T From the data ,...

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