Draw a free body diagram. How many tension forces T are there?
What direction are these tensions in? Is it possible for them to "cancel" each other out?
Do not set the first two equations equal to each other, they are not equal. The two forces acting on the mass, the weight and spring force, add to give the total force which will be zero when x=d.
It seems like you are taking the correct steps. However, I get a different numerical answer than you do.
Also, may I suggest that you don't plug all of those numbers in immediately, and just work with symbols until you have an expression for what it is you are looking for? It'll make the...
A variable to the first power's derivative is equal to one only when differentiating with respect to that variable. So, dh/dh=1, but dh/dt doesn't necessarily.
You don't have to, but you would need to find dh/dt in terms of r and dr/dt and substitute that at some point. Personally I think it...