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

Revision as of 14:50, 2 May 2015


Critically Damped Practice

Practice question for ECE201: "Linear circuit analysis I"

By: Chinar Dhamija

Topic: Critically Damped Second Order Equation


Question

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

ECE201P6.png


Answer

For a response to be critically damped we know that:
$ b^2 - 4c = 0 $
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:
$ b = \frac{1}{RC} $ and $ c = \frac{1}{LC} $

ECE201P6 1.png

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


Questions and comments

If you have any questions, comments, etc. please post them below

  • Comment 1
    • Answer to Comment 1
  • Comment 2
    • Answer to Comment 2

Back to 2015 Spring ECE 201 Peleato

Back to ECE201

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood