A machine weighing 250 lb is mounted on a supporting system consisting of four springs and four dampers. The vertical deflection of the supporting system under the weight of the machine is measured as 0.8 in. The dampers are designed to reduce the amplitude of vertical vibration to oneeighth of the initial amplitude after two complete cycles of free vibration. Find the following properties of the system: (a) undamped natural frequency, (b) damping ratio, and (c) damped natural frequency.

Work = force × a. work b. energy c. distance d. momentum

You are driving directly behind a pickup truck, going at the same speed as the truck. a crate falls from the bed of the truck to the road. (a) will your car hit the crate before the crate hits the road if you neither brake nor swerve? (b) during the fall, is the horizontal speed of the crate more than, less than, or the same as that of the truck?

Athin nonconducting rod with a uniform distribution of positive charge q is bent into a circle of radius r. the central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. a) what is the magnitude of the electric field due to the rod at z = 0? n/c (b) what is the magnitude of the electric field due to the rod at z = infinity? n/c (c) in terms of r, at what positive value of z is that magnitude maximum? r (d) if r = 4.00 cm and q = 9.00 µc, what is the maximum magnitude? n/c