Known to date:

Constant-velocity ineline with m1 and m2

Parallel component of weight is well approximated by weight * slope, for small slopes

Sketch, estimate then ask your calculator for the accurate values of R cos(theta), R sin(theta), arcTan(R_y / R_x), sqrt( R_x ^ 2 + R_y ^ 2).

rubber band and 'rail'

linear approximation to T vs. L

Small-theta approximations:  sin(theta) = tan(theta) = theta