ENSC320-2023Assignment3Part II The place for Laplace-1

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Part II The place for Laplace 2.1 The conjugate pole diagram (a) Sketch, in the complex frequency domain, a pair of poles at . Indicate on the graph, and provide values for, the damping factor, the observable oscillation frequency (damped frequency), and the natural frequency. Give the characteristic equation containing these parameters, and the time domain function in terms of these parameters. Page 11, ensc320-2023, Assignment 3 © Rodney Vaughan, SFU. File: ENSC320-2023_Assignment_3_v4.wpd
(b) Is this system underdamped, critically damped, or overdamped? (c) Sketch or Matlab-draw the time domain signal for when the poles are at (i) (ii) (iii) . For each case, note if it is underdamped, critically damped, or overdamped. Page 12, ensc320-2023, Assignment 3 © Rodney Vaughan, SFU. File: ENSC320-2023_Assignment_3_v4.wpd
2.2 Applying it: differential equations and initial conditions for transient solutions V0=20V, R1=20 Ω L=2mH C=5 μ F The ideal switch (instantaneous with no contact/break bounces) in the circuit has been closed a long time (so there are steady-state conditions, ie., no transients left bouncing around), and it is opened at . (a) Find the initial conditions, . These will be used below. (b) After the switch is opened at :- (i) draw the equivalent circuit. Page 13, ensc320-2023, Assignment 3 © Rodney Vaughan, SFU. File: ENSC320-2023_Assignment_3_v4.wpd
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