A 16 lb weight stretches a spring 6 inches in equilibrium. It is attached to a damping mechanism with constant c. Find all values of c such that the free vibration of the weight has infinitely many oscillations.

Explanation:

Given data:

Weight W = 16 lb

length l = 6/12 = 0.5 ft

hence, spring constant  k = W/l = 16/0.5 = 32 lb/ft

The equation of motion of spring is

the auxiliary equation can be written as

The discriminate of equation is

To get the value of the damping constant,

the independent variable, or the one that is intentionally manipulated is the speed.

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.