Equations - Important Equations from Exam I Natural...

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Unformatted text preview: Important Equations from Exam I Natural Frequency n = 2 f n = s k e m e d = n q 1- 2 For vertical systems n = 2 f n = s g st Period T = 1 f n = 2 n Damping Factor = c 2 m n = c 2 km = c n 2 k Critical Damping c c = 2 m n = 2 km Equation of Motion x + 2 n x + 2 n x = f ( t ) m e Chapter 4 Laplace Transforms L [ g ( t )] = G ( s ) = Z e- st g ( t ) dt The Logarithmic Decrement (p. 147) Period T d = 2 d = 2 n 1- 2 Decrement = 1 p ln x ( t ) x ( t + pT d ) ! = 2 1- 2 Zeta = 1 r 1 + 2 2 1 Chapter 5 Dimensionless frequency = n Dimensionless time = n t D () = (1- 2 ) 2 + (2 ) 2 H () = 1 q D () = 1 q (1- 2 ) 2 + (2 ) 2 () = tan- 1 2 1- 2 ! t () = tan- 1 2 1- 2 2 2- (1- 2 ) ! Frequency Response Function (p. 203) G () = 1 k H () e- j () Transfer Function (p.201) G ( s ) = 1 m ( s 2 + 2 n s + 2 n ) Rotating Unbalanced Mass (p. 205)Rotating Unbalanced Mass (p....
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Equations - Important Equations from Exam I Natural...

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