15.12.1. Unit Step Function u(t−a)

Try these first

1. 1.

   Define the Unit Step Function.

   Hint

   Think about how this function is used to model sudden changes.

2. 2.

   What is the formula for the Laplace transform of the Unit Step Function?

   Hint

   Remember what the exponent represents in relation to time.

3. 3.

   What is the value of u(t−3) when t=2?

   • 0
   • 1
   • Does not exist

   Hint

   Recall the definition of the Unit Step Function.

4. 4.

   The Laplace transform of u(t−a) is given by which formula?

   Hint

   Think of how the exponential decay factor applies.

5. 5.

   A system experiences a load described by f(t) = 5u(t−2) + 3u(t−4). Find the Laplace Transform.

   Hint

   Utilize the linearity property of the Laplace Transform.

6. 6.

   Create a function that applies at t=5 and lasts until t=10 using Unit Step Functions.

   Hint

   Think about how to depict the active window of a function.