Expressing function in terms of unit step function

Question

I have trouble expressing functions in terms of the unit step function, if someone could explain how it works that would be great.

For example -

$g(t) = t^2$ when $0 \le t < 2$

$4$ when $t\ge2$

It could do with some formatting help but I hope you can read understand the question, please ask and I will clarify if not.

Answer 1

$$g(t)=t^2*(H(t)-H(t-2))+4H(t-2)$$

$H(t)$ is the step function (Heaviside). It's not difficult at all, you have just to "draw" the interval with the step function.

• If you multiply a function for $H(t)-H(t-2)$ this means that you "cut" the function in the interval between $0$ and $2$.

• If you multiply the function for just $H(t-2)$ means that the
  function starts at $t=2$ and goes to infinity.