a concave lens has a focal length of -36 cm. find the image distance that results when an object is placed 31 cm in front of the lens.

The image shows a pendulum in simple harmonic motion the pendulum starts at a and swing to e

Astone is thrown into a pond. what happens to the amplitude of the resulting waves as they get farther from the point where the stone hit the water? explain.

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.