If given adequate resources, populations can grow at rapid rates. for example, one female mouse can produce a litter of four to fourteen babies every three to four weeks throughout her life. this population growth would most likely be limited by a. a disease which infects the baby mice shortly after birth. b. an increase in the size of the mice's living space. c. fair weather and a consistent climate. d. a decrease in the local owl population.

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.