View source for Chinar Dhamija Critically Damped Problem ECE201S15 - Rhea

[[Category:ECE201]] 
[[Category:ECE]] 
[[Category:ECE201Spring2015Peleato]]
[[Category:circuits]]
[[Category:linear circuits]]
[[Category:problem solving]]

=Critically Damped Practice=
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'''Practice question for [[ECE201]]: "Linear circuit analysis I" '''
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By: Chinar Dhamija

Topic: Critically Damped Second Order Equation

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==Question==
Find the value for C that will make the zero input response critically damped with roots at -4.

[[File:ECE201P6.png|500px|center]]

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===Answer ===
For a response to be critically damped we know that:<br />
<math>b^2 - 4c = 0</math><br />
The next step would be to simplify the circuit as shown in the image below. Once simplified it becomes a parallel RLC circuit where we know:<br />
<math> b = \frac{1}{RC} </math> and <math> c = \frac{1}{LC} </math>
[[File:ECE201P6_1.png|500px|center]]

Since the root was given to be -4 we can find b.<br />
<math> \frac{-b}{2} = s </math> so we get:  <math> \frac{-b}{2} = -4 </math> therefore b = 8. <br />
Once we know b we can use the critically damped equation to solve for C.<br />
<math>\begin{align}
8^2 - \frac{4}{2C} = 0<br />
64 = \frac{2}{C}<br />
C = \frac{1}{32}<br />
\end{align}
</math>

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==Questions and comments==
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*Comment 1
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