I have the following question (and the beginning of the solution)
I am very confused about signs in this question. When I started solving the question without looking at the answer, I took
$F_{net}=-mgsin\theta + bl\dot \theta $
because the particle is released at an angle $\theta _0$ and therefore its velocity is towards the equilibrium position for the whole motion, and so the drag force is always positive (in the direction of x and theta increasing).
However I look at it, I get that the drag force and the restoring force act in opposite directions in this case when the particle is simply released at rest, so should have opposite signs. I do not understand why in the answer to the question they are given the same signs so that
$F_{net}=-mgsin\theta - bl\dot \theta $
It is causing me some trouble as my choice of sign of the drag force is giving me an $\alpha$ of $-\frac{mg}{bl}$ which would lead to a solution of exponential increase of the angle theta which is clearly not the case!
EDIT: I now understand the signs in the equation here. The velocity and $\dot \theta$ are negative and so using $F_{drag}=-bv$ gives a positive resistive force (as required). However now my confusion just lies in the diagram. I understand that here the arrows are meant to dictate the sign of the force acting (towards equilibrium means you should stick a minus sign in front when using this force in calculations); how would you draw this diagram? My 'free body diagrams' are quite messy I think- I put arrows in and signs in, for example I would draw '$-mgsin\theta $ pointing towards equilibrium and $-bv$ pointing away.
I realise that this is probably seems quite a silly question, but I think I often get the signs wrong because I am not quite sure how to put signs on free body diagrams? How do you use the free body diagrams and is there a resource that goes through some examples?
