Laplace Transform of Periodic Functions Calculator

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Example

Created on 2024-06-20Asked by Sofia Jackson (Solvelet student)

Find the Laplace transform of a periodic function

f(t)

with period

T

Solution

The Laplace transform of a periodic function

f(t)

with period

T

is given by:

\mathcal{L}\{f(t)\} = \frac{1}{1 - e^{-sT}} \int_{0}^{T} e^{-st} f(t) \, dt

Therefore, the Laplace transform of

f(t)

is:

\mathcal{L}\{f(t)\} = \frac{1}{1 - e^{-sT}} \int_{0}^{T} e^{-st} f(t) \, dt

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Elijah Young on Solvelet

1. Find the Laplace transform of the periodic function

f(t) = \cos(2t)

with period

T = \pi

,2. Find the Laplace transform of the function

g(t) = \begin{cases} 1, & -1 \leq t < 0 \\ 0, & t \geq 0 \end{cases}

DefinitionLaplace transform of periodic Functions:- Functions that repeat themselves at regular intervals are called periodic functions. The expression for the Laplace transform of a periodic function f(t) with period T is L{f(t)}=1−e−sT1∫0Tf(t)e−stdt. This characteristic is helpful in analyzing periodic signals in a control system, and signal Processing. Example: Compute the Laplace transform of the periodic square wave f(t) with period T, which can be evaluated using the formula by integrating over one period and multiplied by the periodicity factor 1−e−sT1

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