Laplace to Time Domain Converter: How it works
| Description How it works |
At the heart of this tool is the 2nd order ODE solver. We first solve the differential equation: y" + d1y' + d2 = 1, with the initial conditions y = y' = 0. The solution y of this equation is the step response of the system having laplace transform 1/(s2 + d1s + d2) and the solution y' is the step response of the system having the laplace transform s/(s2 + d1s + d2). Since the Lapalce transform is linear, the inverse Laplace transforms of n2/(s2 + d1s + d2) and n1s / (s2 + d1s + d2) are n2y and n1y' respectively. Finally, using the superposition principle, the inverse laplace transform of (n1s + n2)/(s2 + d1s + d2) is n2y + n1y'. The calculations are done in columns U through AM. See how the 2nd order differential equation solver tool works for details of how the differential equation is solved. |