12. A mass M is free to slide along a frictionless rail. A pendulum of length...

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12. A mass M is free to slide along a frictionless rail. A pendulum of length I and mass rn hangs from M. Find the equations of motion from Lagrange's method. 13. Consider a particle of mass m moving in a plane under the attractive force, mM/r2, directed to the origin of polar coordinates r and O. Determine the Lagrangian equation for the particle. 14. A particle of mass m slides on the inner surface of a cone of half angle a. The axis of the cone is vertical with vertex downward. Gravity g acts vertically downwards. Find the Lagrange's equations of motion in explicit form. 12. A mass M is free to slide along a frictionless rail. A pendulum of length I and mass rn hangs from M. Find the equations of motion from Lagrange's method. 13. Consider a particle of mass m moving in a plane under the attractive force, mM/r2, directed to the origin of polar coordinates r and O. Determine the Lagrangian equation for the particle. 14. A particle of mass m slides on the inner surface of a cone of half angle a. The axis of the cone is vertical with vertex downward. Gravity g acts vertically downwards. Find the Lagrange's equations of motion in explicit form.

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12 From origin coordinates of the mass M in the XY plane is Mx0 and coordinates of mass m hanging ma... View the full answer