A mass weighing 11 lb stretches a spring 4in. The mass is pulled down an additional 3 in and is then set in motion with an initial upward velocity of 5 ft/s. No damping is applied.
(a) Determine the position u of the mass at any time t. Use 32 ft/s² as the acceleration due to gravity. Pay close attention to the units.
(b) Determine the period, amplitude and phase of the motion.

a) , b) , ,

Explanation:

a) The system mass-spring is well described by the following equation of equilibrium:

After some handling in physical and mathematical definition, the following non-homogeneous second-order linear differential equation:

The solution of this equation is:

The velocity function is:

Initial conditions are:

Equations at are:

The spring constant is:

After some algebraic handling, amplitude and phase angle are found:

The position can be described by this function:

b) The period of the motion is:

The amplitude is:

The phase of the motion is:

you can cut your hand off if your not

according to jean piaget, in what stage of cognitive development are children able to understand conservation task?

b. preoperational

just took it