A ring fixed to a support at the top is hanging vertically. A bead of mass m slides through the ring and is connected to the support through a spring of stiffness k as shown in the figure-1. The length of the unstretched spring is almost negligible. Note that gravity acts.
a. Find the equation of motion of the bead using Newton’s laws and find the normal reaction force on the bead.
b. Find the equation of motion of the bead using the work-energy principle.