We observe that the Laplace inverse of this function will be periodic, with period T.

This is because of the part:

We find the function for the first period [f₁(t)] by ignoring the (1 − e^-sT) part:

Now

Considering the second fraction, we have:

,

which we can think of as:

,

So

which is in the form:

,

where a = T.

So we can use Rule (4) again:

and so

This gives

Using Rule (4):

So

So the periodic function with has the following graph: