Transfer Function of ODE using Laplace Transform

Hi.

Hi. I'm wondering if anyone can help me with the process of finding the Transfer functions of some differential equations.

I just don't get it tbh! My lecturer gave us the following very ambiguous example:

Assuming 0 initial conditions:

And apparently the transfer function is given by:

Apparently, this is a representation of a time domain dynamical system, with forcing function , and response function .

Which is fair enough!

But how on earth does that apply to finding the transfer function of, for example, these two:

I'm told that sigma and omega are constants in this case...