Problem 1d correction, hint: Difference between revisions
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For part (d) of problem 1 of Hw#2, every instance of <math>t</math> should be replaced by <math>\tau</math>, so the wording should be changed to read: "Consider the case where <math>\zeta=0</math> and <math>v(\tau)=\sin \omega \tau</math>. Solve for <math>z(\tau)</math>, the normalized output of the oscillator, with initial conditions <math>z_1(0) = z_2 (0) = 0</math>." | For part (d) of problem 1 of Hw#2, every instance of <math>t</math> should be replaced by <math>\tau</math>, so the wording should be changed to read: "Consider the case where <math>\zeta=0</math> and <math>v(\tau)=\sin \omega \tau, \omega > 1</math>. Solve for <math>z(\tau)</math>, the normalized output of the oscillator, with initial conditions <math>z_1(0) = z_2 (0) = 0</math>." | ||
If you've already solved it using <math>t</math> instead of <math>\tau</math> you will get equal credit (it is just a little bit more complex). | If you've already solved it using <math>t</math> instead of <math>\tau</math> you will get equal credit (it is just a little bit more complex). | ||
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To solve this problem, you can use the "method of undetermined coefficients" (see, for example, http://www.efunda.com/math/ode/linearode_undeterminedcoeff.cfm) to solve for the steady-state frequency response solution. Then you can add to it a homogeneous solution that cancels the initial condition from the steady state so that the given initial conditions are satisfied. i.e., find <math>z_{homog.}</math> from <math>z = z_{homog.} + z_{partic.}</math>. | To solve this problem, you can use the "method of undetermined coefficients" (see, for example, http://www.efunda.com/math/ode/linearode_undeterminedcoeff.cfm) to solve for the steady-state frequency response solution. Then you can add to it a homogeneous solution that cancels the initial condition from the steady state so that the given initial conditions are satisfied. i.e., find <math>z_{homog.}</math> from <math>z = z_{homog.} + z_{partic.}</math>. | ||
--[[User:Fuller|Fuller]] 00:32, 15 October 2007 (PDT) | --[[User:Fuller|Sawyer Fuller]] 00:32, 15 October 2007 (PDT) | ||
[Category: CDS 101/110 FAQ - Homework 2] | [Category: CDS 101/110 FAQ - Homework 2] | ||
[[Category: CDS 101/110 FAQ - Homework 2, Fall 2007]] | [[Category: CDS 101/110 FAQ - Homework 2, Fall 2007]] | ||
Latest revision as of 07:34, 15 October 2007
For part (d) of problem 1 of Hw#2, every instance of should be replaced by , so the wording should be changed to read: "Consider the case where and . Solve for , the normalized output of the oscillator, with initial conditions ."
If you've already solved it using instead of you will get equal credit (it is just a little bit more complex).
To solve this problem, you can use the "method of undetermined coefficients" (see, for example, http://www.efunda.com/math/ode/linearode_undeterminedcoeff.cfm) to solve for the steady-state frequency response solution. Then you can add to it a homogeneous solution that cancels the initial condition from the steady state so that the given initial conditions are satisfied. i.e., find from .
--Sawyer Fuller 00:32, 15 October 2007 (PDT)
[Category: CDS 101/110 FAQ - Homework 2]
