Handbook of Laplace Transformation: Fundamentals, Applications, Tables, and Examples

1+as+bs2 2Τζωι A B C A₁ amplitude aT₁ b₁ C₁ characteristic equation coefficients column constant cos Wt D₁ damping ratio denominator derivative differential equation e-at e-bt e-ct e-Zt sin Wt E₁ electrical network example expand f(tn factor function G H I Holzer tabulation initial value input integral K₁ K₂ LAPLACE TRANSFORM PAIRS M₁ mode frequency N₁ original equation R₁ R₂ radians result roots s²/w₁² Section 3.30 Eq shown in Fig sine waves sinusoidal solution solve Substituting T₁ T₁² T₂ T² w₁² T₂² Table tan-¹ tan-1 Tiwi TRANSFORM PAIRS cont transient U₁² U2 Z² U₂² unit impulse unit step voltage w₁ w₁²)² w₁t W²)² W²]² w₂² X₁ yields Z₁)² Z₁² Z₂² zero αζωι εται ζωι Τζωι Τιζωι ωι