background - Background The nutural response of the second...

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Background The nutural response of the second order circuit : The natural response of the second order circuit is derived from the solution of its characteristic differential equation: ….. Where is : B is the damping coefficient Wois the frequency of undamped oscillations of the circuit The type of response derived from the equation above is determined by these two parameters above, and we would be able to figure out these cases: 1) β<ωo that means the response is under the damped. The voltage and the current oscillate with diminishing amplitude. 2) β = ωo the response critically damped. 3) β > ωo the response over the damped The measurement of the natural under damped response: The natural response of under damped circuit is given by this equation: …… Where is : Wd is the frequency of damped oscillations given by this equation : …… Ym and Ф are found from the initial conditions of the circuit in the following equation: ……. We also would be able to express the response in term of damping ratio in this equation :
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This note was uploaded on 03/02/2010 for the course MATH 139 taught by Professor Tall during the Spring '08 term at SIU Carbondale.

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background - Background The nutural response of the second...

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