A mass weighting 16 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 20 lbs when the mass has a velocity of 4 ft/sec. Suppose the object is displaced an additional 7 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds.

The equation for the object's displacement is

Explanation:

Given:

m = 16 lb

δ = 3 in

The stiffness is:

The angular speed is:

The damping force is:

Where

FD = 20 lb

u = 4 ft/s = 48 in/s

Replacing:

The critical damping is equal:

Like cc>c the system is undamped

The equilibrium expression is:

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.