Purchase Solution

Laplace Transform of a periodic function

Not what you're looking for?

Ask Custom Question

See the attached file.
Let f be a piecewise continuous function on [0,T]. Define f on the whole of [0,inf) by f(t+nT) for all t and all integer n. Show that the Laplace transform if f is given by

L[f(t)] = 1/[1-exp(-sT)]*int(exp(-st)*f(t)dt,t=0..T)

By taking the Laplace transform and using the convolution theorem, obtain the solution of the integral equation

f(t) = 1+t+int[(t-u)f(u)du,u=0..t).

Purchase this Solution

Solution Summary

The solution shows how to use the Laplace transform definition and convolution properties to obtain the required results.

Solution Preview

Please see the attached file.

You might want to check out ...

Purchase this Solution

Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.