Two Pendula on 70cm Strings Collision Angle

[Sean77771]

Homework Statement

Two pendula are suspended on 70cm strings connected at the same point on a ceiling. The mass on the left is 45g and is held so the string makes an angle of 10 degrees with the vertical. The mass on the right is 65g and is held in the opposite direction so the string makes an angle of 4.2 degrees with the vertical. When the masses are released, what is the value of the angle where they collide?

Homework Equations

Pendula equations

The Attempt at a Solution

I have no idea how to figure this out. I am pretty sure that the periods of the pendula are independent of their masses, which would lead me to believe that they would collide at an angle of 0 (right on the vertical) but I don't know how to prove this.

 

[catkin]

I agree. Even using the more accurate formula for larger amplitudes(http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.html#c1) the error of the simple formula for the 10 degree pendulum is less than 0.2%