A particle of mass m is suspended from a support by a light string of length which passes through a small hole below the support (see diagram below). The particle moves in a vertical plane with the string taut. The support moves vertically and its upward displacement (measured from the ring) is given by a function z = h(t). The effect of this motion is that the string-particle system behaves like a simple pendulum whose length varies in time. TH z=h(t) [Expect to use a few lines to answer these questions.] a) Write down the Lagrangian of the system. b) Derive the Euler-Lagrange equations. c) Compute the Hamiltonian. Is it conserved?

A particle of mass m is suspended from a support by a light string of length which passes through a small hole below the support (see diagram below). The particle moves in a vertical plane with the string taut. The support moves vertically and its upward displacement (measured from the ring) is given by a function z = h(t). The effect of this motion is that the string-particle system behaves like a simple pendulum whose length varies in time. TH z=h(t) [Expect to use a few lines to answer these questions.] a) Write down the Lagrangian of the system. b) Derive the Euler-Lagrange equations. c) Compute the Hamiltonian. Is it conserved?