Good day I am currently determining the laplace transform of this equation with $q$ as the output angle and $T$ as the input torque to the system.
$$T = a \dfrac{d(q)}{dt} + b \cos(q)$$
and from my understanding, the Laplace transform of a derivative of a function $f$ is just
$$\frac {df(t)}{dt} \mapsto sF(s) - f(0)$$
and the derivative of a cosine function of $t$ is just
$$\cos(at) \mapsto \frac s {(s^2 + a^2)}$$
However my goal is to get the transfer function $\dfrac{Q(s)}{T(s)}$
From
$$T(t) = \left(a\dfrac {dq(t)}{dt}+b\cos(q(t))\right)$$
I am confused on whether I should do a linear approximation of $\cos(q(t))$ to make it $q(t)$ instead or consider $q$ as the variable itself instead. But if I do the latter, how do I factor out $Q(s)$ after performing the Laplace transform as the $q$ will just become $s$.