Midterm equation sheet

# Midterm equation sheet - Equation Sheet for 351 Midterm...

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Equation Sheet for 351 Midterm Exam, Fall 2009 1 1 xx dy K(x ) dx = ⎛⎞ = ⎜⎟ ⎝⎠ f = 1/T = ω/ 2 π Y( ) A( ) iB( ) ω ωω i ec o s i s i n θ =− 2 1 2 1 t t t t y(t )dt y dt = 1 1 N i i yy N = = 2 1 2 21 t t rms yd t y tt = 2 1 1 N rms i i N = = 0 max min ry y 0 100 down up h %e * r = 0 100 L L y(x) y (x) * r = 0 2 100 x R S * r = 0 1 nn n y(t ) A ( A cos nt B sinnt ) = =+ + 0 1 n A ( A cos n t B sin nt ) = + 0 1 n n A C sin( t ) φ = + 22 n CA B n n n A tan B = 2 0 2 1 T/ Ay ( t ) d t T = 2 2 2 n A y(t )cos n tdt T = 2 2 2 n B y(t )sinn tdt T = A( ) y( t )cos tdt −∞ = B () y ( t ) s i nt d t −∞ = 2 1 2 N ir k / N k r Y( f ) y(r t)e N π δ = = it ) y(t)e dt −∞ 2 if t −∞ = 2 1 2 t Y( f )e df −∞ i(f) Y( f )e ϕ = [][] Y(f) ReY(f) ImY(f) [ ] [] 1 (f) tan = 1 11 0 1 dy d y d y a a ... a a y F(t ) dt dt dt ++ + + = yK F ( t ) = , yyK F ( t )K A U ( t ) τ += = ± 0 t/ KA ( y KA)e =+− F ( t A s i = ± 1 2 1 KA Ce sin t tan ωτ −− + 2 1 1 M( ) = + , 1 ()M 2 12 y K F ( t ) ς = ±± ± 0 2 1 n t d e KA ( y KA) cos t ςω

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Midterm equation sheet - Equation Sheet for 351 Midterm...

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