1. A pendulum consist of a particle with mass M attached to a massless piece of string of length l which is suspended from the bottom of a spring with spring constant k. The spring is guided within a column such that the connection to the pendulum can only move vertically. Referring to the illustration below, let z represent the amount the spring is stretched. Determine a) the Lagrangian for the system in terms of the two independent coordinates 0 and z.and b) the equation of motion for just the z-coordinate. Rem: the equation of motion is the diff eq, not the solution to the diff eq.

1. A pendulum consist of a particle with mass M attached to a massless piece of string of length l which is suspended from the bottom of a spring with spring constant k. The spring is guided within a column such that the connection to the pendulum can only move vertically. Referring to the illustration below, let z represent the amount the spring is stretched. Determine a) the Lagrangian for the system in terms of the two independent coordinates 0 and z.and b) the equation of motion for just the z-coordinate. Rem: the equation of motion is the diff eq, not the solution to the diff eq.