ECE2260F09_HW5p1dsoln

ECE2260F09_HW5p1dsoln - L e − at cos ω t = s a s a 2 ω...

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2260 F 09 HOMEWORK #5 prob 1d solution E X : Find the Laplace transform of the following waveform: f ( t ) = e 5 t [2cos(12 t ) + 7sin(12 t )] S OL ' N : The Laplace transform is linear, meaning that we may multiply basic transform pairs by constants to obtain new transform pairs. Also, we may transform the terms of a sum individually and sum the results in the Laplace domain. L e 5 t [2cos(12 t ) + 7sin(12 t )] { } = 2 L e 5 t cos(12 t ) { } + 7 L e 5 t sin(12 t ) { } We find the following transform pairs in tables:
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Unformatted text preview: L e − at cos( ω t ) { } = s + a ( s + a ) 2 + ω 2 L e − at sin( ω t ) { } = ω ( s + a ) 2 + ω 2 Applying the above transform pairs yields the following result: L e − 5 t [2cos(12 t ) + 7sin(12 t )] { } = 2 s + 5 ( s + 5) 2 + 12 2 + 7 12 ( s + 5) 2 + 12 2 or L e − 5 t [2cos(12 t ) + 7sin(12 t )] { } = 2 s + 94 ( s + 5) 2 + 12 2...
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