Number 12.46. 12.47. Please help me 12. and a are constants and Z is the vertical axis.

Number 12.46. 12.47. Please help me

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12. and a are constants and Z is the vertical axis. 12.46. A pendulum of mass m and length l is suspended from a car of mass M that moves with velocity u on a frictionless horizontal overhead rail. The pendulum swings only in the vertical plane contain- ing the rail. (a) Set up the Lagrangian L and the Hamiltonian H. (b) Show that there is one cyclic (ignorable) coordinate. Eliminate this coordinate and discuss the motion. 12.47. A mass m ticd to a vertical spring of spring constant k and vertical length has a constant upward acceleration ag- The acceleration due to gravity is g. Find the Lagrangian and the equations of mo- tion Calculate the Hamiltonian function, and write Hamilton's cquations. What is the time period of the motion? ntml ficld attractiye force of magnitude [k/r]e-a", where k and wotions of 12. and a are constants and Z is the vertical axis. 12.46. A pendulum of mass m and length l is suspended from a car of mass M that moves with velocity u on a frictionless horizontal overhead rail. The pendulum swings only in the vertical plane contain- ing the rail. (a) Set up the Lagrangian L and the Hamiltonian H. (b) Show that there is one cyclic (ignorable) coordinate. Eliminate this coordinate and discuss the motion. 12.47. A mass m ticd to a vertical spring of spring constant k and vertical length has a constant upward acceleration ag- The acceleration due to gravity is g. Find the Lagrangian and the equations of mo- tion Calculate the Hamiltonian function, and write Hamilton's cquations. What is the time period of the motion? ntml ficld attractiye force of magnitude [k/r]e-a", where k and wotions of