Laplace Transforms

Application of Laplace Transform

Application of Laplace Transform: Application of Laplace Transform methods are used to find out transient currents in circuits containing energy storage elements. To find these currents, first the differential equations are formed by applying Kirchhoff’s laws to the circuit, then these differential equations can be easily solved by using Laplace transformation methods. Consider a series …

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Laplace Transform Partial Fraction

Laplace Transform Partial Fraction: Most transform methods depend on the partial fraction of a given transform function. Given any solution of the form N(s) = P(s)/Q(s), the inverse Laplace transform can be determined by expanding it into partial fractions. The Laplace Transform Partial Fraction depend on the type of factor. It is to be assumed …

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Inverse Transformation

Inverse Transformation: We already discussed Laplace transforms of a functions f(t). If the function in frequency domain F(s) is given, the Inverse Transformation can be determined by taking the partial fraction expansion which will be recognizable as the transform of known functions. Laplace Transform of Periodic Functions: Periodic functions appear in many practical problems. Let …

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Laplace Theorem

Laplace Theorem: The Laplace theorem is given by Differentiation Theorem Integration Theorem Differentiation of Transforms Integration of transforms First Shifting Theorem Second Shifting Theorem Initial Value Theorem Final Value Theorem (a) Differentiation Theorem: If a function f(t) is piecewise continuous, then the Laplace transform of its derivative d/dt [f(t)] is given by (b)Integration Theorem: If …

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Laplace Properties

Laplace Properties: Laplace transforms have the following Laplace Properties. (a) Superposition Property: The first Laplace Properties is Superposition Property. The Laplace transform of the sum of the two or more functions is equal to the sum of transforms of the individual function, i.e. if Consider two functions f1(t) and f2(t). The Laplace transform of the …

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Definition of Laplace Transform

Definition of Laplace Transform: The Definition of Laplace Transform is used to solve differential equations and corresponding initial and final value problems. Laplace transforms are widely used in engineering, particularly when the driving function has discontinuities and appears for a short period only. In circuit analysis, the input and output functions do not exist forever …

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