Question

A block (mass m₁) E can move horizontally on a smooth surface (Fig. ). A simple pendulum (mass m₂) is connected to the block by a pin. Find the equations of motion using the Lagrange formalism.

Answer 1

The system is conservative; it has two degrees of freedom. We use the generalized coordinates x and ϕ as shown in the figure. With the zero-level of the potential of the force m₂g chosen at the height of the mass m₁, we have 

into the Lagrange equations

yields the coupled equations of motion