Two small masses are connected via strings and are moving in the manner of a conical pendulum, as depicted below. For this problem, we will assume that the two segments of string are along the exact same direction, such that the fixed point, $m_1,$ and $m_2$ all lie along a straight line. The rope forms an angle, $,$ with the vertical direction, $m_1$ traces out a horizontal circle of radius $r_1,$ and $m_2$ traces out a horizontal circle of radius $r_2.$

a$.$ To get a feel for the problem, let's first analyze it if it were stationary $($i$.$e$.,$ no circular motion just yet $-$ it just hangs straight down.$)$ What is the force of tension in the bottom wire? What about the top wire? Do your answers make sense? Why?

b$.$ Now suppose the masses are swinging in the manner of a conical pendulum, as pictured. Both wires form a straight line. Write down Newton's $2^{nd}$ Law equations for each coordinate direction for each mass. You should have a total of $4$ equations.

c$.$ Can you determine the force of tension in the bottom wire in terms of the given quantities $m_1,m_2,r_1,r_2,,$ and constants?

d$.$ What about the top wire?

e$.$ Determine the speed, $v_1,$ of the upper mass in terms of the given quantities $m_1,m_2,r_1,r_2,,$ and constants.