Step Response
In general $F_{ap}(s)$ can have poles of its own and thus the system response to will reflect the poles of both the transfer function, $H(s)$, and the LT of the forcing term $F_{ap}(s)$.

The effects of the transfer function are present for any input so it is particularly important to understand the effects of the poles (and zeros) of $H(s)$.

We will mostly look at the cases where the input is a unit impulse, $δ(t)$, or a unit step, $u(t)$. Recall from A3 Q3 that for a second order DE these terms allow us to effectively set the initial condition at 0+ of for the system.

The response to the unit impulse is $Y(s)=H(s)$

The response to the unit step impulse is $Y(s)=s1 H(s)$

The step response is the integral of the impulse response
In the “real world” it is often easier to physically generate a unit step function than a unity impulse so point 2 above gives us a nice way to compute transfer functions.