Tyrone is interested in conducting a study to investigate what type of dog food dogs prefer. He selects two brands of canned dog food: Brand A, a chicken-based dog food; and Brand B, a beef-based dog food. In the morning, he feeds 20
dogs Brand A and records how much food is left after one hour. In the afternoon, he feeds 20 different dogs, of the same
age and type, Brand B. Again, he records how much food is left after one hour. He finds that cats eat significantly more of
Brand B than Brand A.
What type of design has Tyrone used in his study?

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.