For the simple pendulum and double pendulum in $2$ D as shown below, let the mass center be at the midpoint of each link. Define the Cartesian coordinate system by drawing on your answer sheet and state the degree of freedom $(5\%),$ and

$(1)$ Write the equation relating the mass center coordinate $(($:$x_1,y_1\}$

$(2)$ Write the equation relating the mass center coordinate $(x_1,y_1)$ and $(x_2,y_2)(10\%)$