# Function in terms of Heaviside functions

Discussion in 'Homework Help' started by xxxyyyba, Aug 16, 2013.

1. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
283
6
Hi!
My task is to write function below in terms of Heaviside functions:

Here is my solution:

Is it correct?

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
Looks fine to me.

3. ### WBahn Moderator

Mar 31, 2012
20,232
5,755
Yes.

Look at the result and see if the answer makes sense. You should note that each time a term is turned on that the coefficient represents an amount by which the function immediately changes. Do those changes make sense when compared to the original function?

You also want to get in the habit of doing sanity checks to be more confident of your own work (or in checking the work of others). In this case an easy one is to check to be sure that the function works for t<<0 and t>>0. For t<<0 all of the step functions are turned off yielding zero and (since there are no surviving terms) for t>>0 all of the step functions are turned on, again yielding zero (because the sum of all the terms is zero).

4. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
283
6
Thanks a lot for replies!