I have a set of equations from which I have to find the transfer function $G\left(s\right)=\frac{y\left(s\right)}{u\left(s\right)}$
I am given:
$0.15\cdot \frac{d^2\left(x+l\theta \right)}{dt^2}+1.4715\sin \left(\theta \right)=0$
and
$\frac{d^2x}{dt^2}+0.15\frac{d\left(x+\theta \right)}{dt^2}+0.5\frac{dx}{dt}=u$
I am also given that $y=x+\theta $
Basically, by simplifying, I get:
$\frac{dx^2}{dt}+0.5\frac{dx}{dt}-1.4715\theta =u$
and
$0.15\frac{d\theta ^2}{dt}+1.4715\theta +0.15\frac{dx^2}{dt^2}=0$
How do I go about finding the transfer function? $x$ and $\theta$ are in the same equation. Do I simply transfer them both as $X(s)$ and $\theta(s)$?