Show that the center of gravity of the arc of the cycloid x=aθ+Sinθ and y=aθ-Cosθ in the positive quadrant is describe below:[(π-4/3)*a, 2/3*a]

Question

Show that the center of gravity of the arc of the cycloid  x=aθ+Sinθ and y=aθ-Cosθ in the positive quadrant is describe below:[(π-4/3)*a, 2/3*a]

JACQUES D. · Accepted Answer

The cycloid equation should have y = a-cosθ

Find area = integral of y (dx/dθ) dθ from 0 to first intercept.

Find the weighted moments by integrals xy (dx/dθ)dθ and y²(dx/dθ)dθ

COG are integral of xdA/ integral of dA and integral of ydA/integral of dA

Show that the center of gravity of the arc of the cycloid x=aθ+Sinθ and y=aθ-Cosθ in the positive quadrant is describe below:[(π-4/3)a, 2/3a]