exam02_sample_problems

# exam02_sample_problems - 2 Name PROBLEM NO 1(50 Analogous...

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March 30, 2004 Name __________________ 2 PROBLEM NO. 1 (50%) Analogous two-degree-of-freedom mechanical and electrical systems are shown in the figure below: (a) For the mechanical system, determine the system equations in the time domain by: (i) Drawing the free body diagrams (ii) Writing the elemental equations (iii) Combining the elemental equations to find two governing differential equations (iv) Converting the ODEs from part (iii) into differential equations with velocities and (and derivatives) as the output variables and force F(t ) (and possibly its derivative) as the input variable. b x x i i

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March 30, 2004 Name __________________ 3 PROBLEM NO. 1 (Continued) (b) For the electrical system, determine the two system equations in the time domain using the loop method. You should get one differential equation for each loop, in terms of i 1 and i 2 (and their derivatives, and input voltage E ( t ) (and possibly its derivative). (c) Given that for the mechanical system the Effort variable is Force and the Flow variable is Velocity, and that for the electrical system the Effort variable is Voltage and the Flow variable is Current; identify the corresponding elements between the mechanical and the electrical systems and the corresponding impedance terms. (Recall impedance is the Effort variable divided by the Flow variable.) Mechanical System Mechanical impedance Electrical System Electrical impedance Displacement ( x ) ------------------- Charge ( q ) ----------------------- Force ( F ) ------------------ Voltage ( e ) ----------------------- Velocity ( v ) ------------------- Current ( i ) ----------------------- Mass ( m ) Spring ( k ) Dashpot ( b )
March 30, 2004 Name __________________ 4 PROBLEM NO. 2 (50%) Given the transfer function , draw the Bode straight line approximation using the following steps: (a) Find the poles, zeros, and static gain of the transfer function G ( s ). (b) Write all first order terms in the form ( ! s +1) (except s or 1/ s ) and all second order complex terms in the form . (c) Provide the break frequencies for all of the terms in transfer function G ( s ). (d) Plot magnitude and phase of all elemental transfer functions separately on the graphs on the next page. Label the elemental transfer functions on the graph along with all break frequencies and slopes. (e) Plot the total transfer function made up of the elemental transfer functions in part (d).

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March 30, 2004 Name __________________ 5 0.0 1 0. 1 1 10 100 1 . 10 3 1 . 10 4 1 . 10 5 100 80 60 40 20 0 20 40 60 80 100 Bode Plot-Phase Frequency (rad/s) Phase (deg) 0.0 1 0.1 1 10 10 1 . 10 3 1 . 10 4 1 . 10 5 30 26 22 18 14 10 6 2 2 6 10 Bode Plot- Magnitude Frequency (rad/s) Magnitude (dB)
March 30, 2004 Name __________________ 6 PROBLEM NO. 2 (Continued) (f) For G ( s ) given on the previous page, write down expressions for the magnitude and phase of the frequency response as a function of !

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exam02_sample_problems - 2 Name PROBLEM NO 1(50 Analogous...

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