Let g denote the acceleration due to gravity and a > 0. A particle of mass m glides (without friction) on the cycloid given by x = a(θ - sin θ), y = a(1 + cos θ), with 0 ≤ θ ≤ 2 π. Then the equation of motion of the particle is
1
\((1-\cos \theta) \ddot{\theta}+\frac{1}{2}(\sin \theta)(\dot{\theta})^2\) - \(\frac{g}{2 a} \sin \theta=0\)
2
\((1-2 \cos \theta) \ddot{\theta}+(\sin \theta)(\dot{\theta})^2\) - \(\frac{g}{a} \sin \theta=0\)
3
\(m(1-2 \cos \theta) \ddot{\theta}+(\sin \theta)(\dot{\theta})^2\) + \(\frac{g}{a} \sin \theta=0\)
4
\(m(1-2 \cos \theta) \ddot{\theta}+\frac{m}{2}(\sin \theta)(\dot{\theta})^2\) - \(\frac{g}{a} \sin \theta=0\)