Example 2: Newton’s 2^nd law

A bead of mass m moves on a bar. The bar is shaped as shown in the figure so that . If the bar is smooth and the particle is released from rest at the position , calculate the equation of motion of the bead and the force applied by the bar on the bead at .

Solution:

Kinematics relation:

Kinetics:

Equation of motion:

Subtract to get