I am learning about control theory.
Let's consider this system.
$$ m a(t) + b v(t) + k x(t) = f(t) $$
$a$ is acceleration
$v$ is velocity
$x$ is displacement
$f$ is external force
In my textbook, in chapter about "state space model" , two state variables ($x$ and $v$) are necessary
to completely describe this system.
However, I think $x$ can completely describe this mass's motion by itself.
If we know $x$, $v$ can derived from $x$.
So I have two questions.
- Why two variables are needed.
- Why "$x$ and $v$" ? Can "$v$ and $a$" or "$x$ and $a$" also describe this system ?