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ECE2260F09_HW5

# ECE2260F09_HW5 - s 2 b F s = 4 s 2 17 s 16 s 3 4 s 2 4 s c...

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2260 F 09 HOMEWORK #5 1. Find the Laplace transforms of the following waveforms: a) f ( t ) = e a ( t −τ ) u ( t − τ ) where τ > 0 b) t 2 d dt e 4 t cos(3 t ) [ ] c) sin(5 t ) t dt 0 t Hint: d dx tan 1 ( x ) = 1 x 2 + 1 d) f ( t ) = e 5 t [2cos(12 t ) + 7sin(12 t )] 2. Show that the following identity is valid for a > 0: L { f ( at )} = 1 a F s a 3. Find the inverse Laplace transform for each of the following expressions: a) F ( s ) = 6 s 3 19 s 2 + 42 s + 72 s 4 + 7 s 3 + 12 s
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Unformatted text preview: s 2 b) F ( s ) = 4 s 2 + 17 s + 16 s 3 + 4 s 2 + 4 s c) F ( s ) = − − s 3 − 36 s 2 − 863 s − 6900 ( s 2 + 24 s + 400)( s 2 + 24 s + 225) d) F ( s ) = s 2 + 11 s + 37 s 2 + 8 s + 25 4. Find the Laplace transform of t n . 5. Find the inverse Laplace transform of 1 s n ....
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