pendulum

Since the bob travels in a circular path, x2 + y2 = L2

and C is the distance between the points (x,y) and (0,-L)

which is ( )x-02+( )y-(-L) 2 = x2+( )y+L2

= L2-y2 +( )y+L2 = 2L2+2Ly = 2L L+y

Thus, it is no surprise that the plot of the chord length as a function of horizontal

displacement is the plot of the square root function given above.

 

—excerpt from MATHEMATICAL EXPLORATIONS WITH A PENDULUM, Richard Kick

 

Done