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.

Astone is thrown with a speed v0 and returns to earth, as the drawing shows. ignore friction and air resistance, and consider the initial and final locations of the stone. which one of the following correctly describes the change δpe in the gravitational potential energy and the change δke in the kinetic energy of the stone as it moves from its initial to its final location? options a.δpe = 0 j and δke = 0 j b.δpe is positive and δke is negative c.δpe = 0 j and δke is positive d.δpe is negative and δke is positive e.δpe = 0 j and δke is negative