Handbook of Laplace Transformation: Fundamentals, Applications, Tables, and Examples |
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Page 64
... initial value of the voltage across the capacitance . Next , solve ( 3.51-3 ) for the Laplace transform of the ... conditions are omitted in writing the equations for a circuit because they can be added later and because they are unnecessary ...
... initial value of the voltage across the capacitance . Next , solve ( 3.51-3 ) for the Laplace transform of the ... conditions are omitted in writing the equations for a circuit because they can be added later and because they are unnecessary ...
Page 79
... initial conditions are inserted in ( 3.62-6 ) , it will be found that * is initially –32.2 ft / sec , or one g . Transforming ( 3.62-6 ) , 3.11 ( s2 3.11 ( 82Xsx 。— xo ) + 2 ( sX- xo ) + 2 ( sX − xo ) + 1000+ 1000 100 S 0 ( 3.62-7 ) ...
... initial conditions are inserted in ( 3.62-6 ) , it will be found that * is initially –32.2 ft / sec , or one g . Transforming ( 3.62-6 ) , 3.11 ( s2 3.11 ( 82Xsx 。— xo ) + 2 ( sX- xo ) + 2 ( sX − xo ) + 1000+ 1000 100 S 0 ( 3.62-7 ) ...
Page 81
... initial conditions are x 。= 0 , xo = in ( 3.62-7 ) yields -16.1 . Inserting these values -100 3.11 ( 16.1 ) X = ( 3.62-21 ) s ( 3.11s 2s + 1000 ) ( 3.11 s2 + 28 + 1000 ) which is the same as ( 3.62-8 ) except that an additional term is ...
... initial conditions are x 。= 0 , xo = in ( 3.62-7 ) yields -16.1 . Inserting these values -100 3.11 ( 16.1 ) X = ( 3.62-21 ) s ( 3.11s 2s + 1000 ) ( 3.11 s2 + 28 + 1000 ) which is the same as ( 3.62-8 ) except that an additional term is ...
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1+as+bs2 2Τζω A₁ amplitude applied aT₁ b₁ C₁ coefficients column constant cos Wt D₁ damping damping ratio dashpot denominator derivative determinant differential equations e-at e-bt e-ct e-wit e-Zt sin Wt E₁ electric network example f(tn factor fi(t final value force function Holzer tabulation initial value input integral K₁ K₂ LAPLACE TRANSFORM PAIRS M₁ mass mechanical system missile mode frequency numerical values obtained R₁ R₂ radians radians/sec recurring waveform result roots s²/w₁² shown in Fig sine waves sinusoidal solution solve spring constant Substituting T₁ T₁² T₂ T² w₁² T₂² Table tan-¹ tan-1 Tiwi TRANSFORM PAIRS cont transient U₁² U₂² unit impulse unit step value theorem voltage w₁ w₁t W²)² w₂² X₁ yields Z₁)² Z₁² zero αζωι εται ζωι Τζωι Τιζωι