Acontinuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. the wave has frequency 62.0 hz, amplitude 5.20 mm and wavelength 0.560 m.

(a) how long does it take the wave to travel a distance of 8.40 m along the length of the string?

(b) how long does it take a point on the string to travel a distance of 8.40 m, once the wave train has reached the point and set it into motion?

(c) in parts (a) and (b), how does the time change if the amplitude is doubled?

Which statement best describes how private industry decides where to spend the money on research and development

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.

Anonconducting sphere of radius r=11.2 cm has a volumic charge density that varies explicitly with r like ρ=br for r