The transfer function (or impulse response) of a linear system is the complete characterization of the system. Once it is known, the output to the system may be determined by two methods:

Method 1: Multiplying the transformed impulse response and inputs and taking the inverse Laplace transform to yield the time-domain output.

Method 2: Performing the time-domain convolution of the inverse Laplace transformed transfer function and the input waveform.

Typically Method 1 is the preferred method, as many EE students studying introductory Linear Systems will attest to.