Astring with tension ft= 10 n, with one end pinned and the other end free, is used to produce a wave supplied by a driving frequency. (a) if the frequency with which you produce waves is f= 10khz and the wavelength of the wave is a = 0.01 m, what is the velocity with which the wave? (5 points) (b) what is the period of the wave? (5 points) (c) what is the linear mass density of the string? (5 points)

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.