Example 2: A beam of light enters the flat surface of a diamond at an angle of 30° from the normal.
The angle of refraction in the diamond is measured to be 12° from the normal. Determine the speed of
light in the diamond
bar

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.