g A 4 lb weight stretches a spring 2 ft in equilibrium. It is attached to a damping mechanism with constant c. (a) Find the value of c for which the motion is critically damped. (b) If the motion is critically damped, find the displacement y(t) when the spring is initially displaced 6 inches above equilibrium and given a downward velocity of 3 ft/sec.

Solution :

Given :

Weight = 4 lb

Stretched of a spring in  equilibrium,Δ = 2 ft

a). We know that

F = kΔ

4 = k x 2

k = 2 lb/ft

∴ Stiffness of the spring is, k = 2 lb/ft

Motion is critically damped.

C = 0.99729 lb.s/ft.

b). Displacement

Initial displacement = 6 inches

Therefore, displacement :

  the unit of the measure =

explanation:

  the property that is quantified by the energy needed per of material to raise the temperature by one.

  si unit of energy = joule (j)

  si unit of temperature = kelvin (k)

  si unit of mass of material = kilogram (kg)

the property that is quantified by the energy needed per of material to raise the temperature by one is called specific heat.

the unit of specific heat is