Explore BrainMass

Laplace Transform of a periodic function

This content was STOLEN from BrainMass.com - View the original, and get the solution, here!

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).

© BrainMass Inc. brainmass.com September 21, 2018, 5:51 am ad1c9bdddf - https://brainmass.com/math/linear-transformation/laplace-transform-periodic-function-24736


Solution Preview

Please see the attached file.

You might want to check out ...

Solution Summary

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