(b) consider a pendulum of mass m oscillating in a vertical plane, whose (weightless) string is elastic with spring constant k and length , before extension.

(b) Consider a pendulum of mass m oscillating in a vertical plane, whose (weightless) string is elastic with spring constant K and length , before extension. Write down the Lagrangian of the system, mentioning the generalised coordinates. C) Prove that, if the Lagrangian of an unconstrained system is invariant under continuous translation, then the total linear momentum is conserved.