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| − | The response to cos(2t) is | + | The response to cos(2t) can be broken up into to parts because <math>cos(2t) = \frac{e^{2jt} + e^{-2jt}}{2}</math>. |
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| + | The response due to <math>\ e^{2jt}</math> is <math>\ te^{-2jt}</math> | ||
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| + | The response due to <math>\ e^{-2jt}</math> is <math>\ te^{2jt}</math> | ||
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| + | Placing the responses into the equation we get <math>\frac{te^{-2jt} + te^{2jt}}{2}</math> which is equal to <math>\ tcos(2t)</math>. | ||
Latest revision as of 13:10, 19 September 2008
The response to cos(2t) can be broken up into to parts because $ cos(2t) = \frac{e^{2jt} + e^{-2jt}}{2} $.
The response due to $ \ e^{2jt} $ is $ \ te^{-2jt} $
The response due to $ \ e^{-2jt} $ is $ \ te^{2jt} $
Placing the responses into the equation we get $ \frac{te^{-2jt} + te^{2jt}}{2} $ which is equal to $ \ tcos(2t) $.
