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# 2 n 2 s 2 2 n s n 20 1 s s a 2 2 21 2 n 2 s

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Unformatted text preview: (α − b) α − e + (b − a ) (b − a ) sin (ω t ) cos (ω t ) 2 ω ( s + a )2 + ω 2 (s + a) ( s + a )2 + ω 2 s +α ( s + a)2 + ω 2 19. 2 ωn 2 s 2 + 2ζ ω n s + ω n 20. 1 s ( ( s + a) 2 + ω 2 ) 21. 2 ωn 2 s ( s 2 + 2ζωn s + ω n ) 22. (s + α ) s ( ( s + a)2 + ω 2 ) 23. 1 ( s + c) ( ( s + a ) 2 + ω 2 ) −bt e α2 +ω2 ω −1 sin (ω t + φ ) , φ = tan (ω / α ) e − at sin (ω t ) e − at cos (ω t ) 1 ω (α − a ) 2 + ω 2 e − at sin (ω t + φ ) , φ = tan −1 ω α − a ωn e− (ζω n t ) sin ω n 1 − ζ 2 t , ζ < 1 2 1−ζ ( ) − at 1 −1 1 + e sin (ω t − φ ) , φ = tan (ω −a ) 2 2 a + ω ω a2 + ω 2 1 − (ζω t ) −1 e n sin ω n 1 − ζ 2 t + φ , φ = cos (ζ ) , ζ < 1 1− 1−ζ 2 (( α 1 + 2 2 a +ω ω )) (α − a )2 + ω 2 − at ω −1 ω e sin (ω t + φ ) , φ = tan −1 − tan 2 2 a +ω α −a −a e − at sin (ω t + φ ) e − ct − 2 2 (c − a ) + ω ω (c − a ) 2 + ω 2 , φ = tan −1 ω a−c...
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## This note was uploaded on 04/04/2014 for the course ME 3600 taught by Professor Kamman during the Spring '09 term at Western Michigan.

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