pretty new to this concept, so do bear with me.
A linear dynamic system is described by the following differential equation:
Transfer function H(s) is calculated to be =
I've already found the transfer function by assuming that the initial conditions are set to 0, getting the calculated stuff as shown above. I will then inverse Laplace it in order to find h(t), which turns out to be (exp^(-4t)t)
I will then use the formula, which is :
This is what I got, and I was wondering if it is correct:
If so, why did the questions give me the initial conditions? What should I do with them? Also, how do I determine whether the system is stable? Unclear of this.
Thanks :)
As per EDIT:
I've converted them into differential equations where by:
In this case, how do I find the TF? I'm supposed to divide by X(s) in both sides, but the equation on the right will have a problem won't it?