**24. A tray is moved horizontally back and forth in simple harmonic motion at a frequency of ƒ = 2.00 Hz. On this tray is an empty cup. Obtain the coefficient of static friction between the tray and the cup, given that the cup begins slipping when the amplitude of the motion is 5.00 × 10-2 m.

You pull on a string with a horizontal force of magnitude Fyb = 69 N that is attached to a block of mass m 6 kg, then to the axle of a solid cylinder of mass me = 4.4 kg and radius r = 0.5 m, then to a spring of spring constant k = 115 N/m. This is all done on an inclined plane where there is friction (μs = 0.65 and μk = 0.36), and the incline angle is 0 = 30 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. k lllllllll Fyb b 0 Speed First, what is the speed of the block and cylinder after you have pulled the block and cylinder 172 cm down the plane? V=

A spring is attached to a block with a mass of 2.33 kg. The block is set on a rough horizonal surface, and you pull horizontally on the other end of the spring, steadily increasing the force. As soon as the spring stretches 0.126 m beyond its equilibrium length, you notice the block starts to move. If the spring constant is 75.8 N/m, what is the coefficient of static friction between the block and the surface?

A 3 kg block attached to a spring with a spring constant of 9 N/m oscillates horizontally on a frictionless table. Its velocity is 7 m/s when x0 = 0.39 m. What is the block's maximum acceleration (in m/s^2)?