a) i) The mechanical energy E_mec is given by:

When k=U

Therefore, the displacement of the oxygen atom when k=U is

ii) Also, when k=U

Therefore, the velocity of the oxygen atom when k=U is

b) i)During a given period the oxygen kinetic energy equals the potential energy 4 times. Twice at and twice at

The time that separates the two consecutive positions and is obtained as follows:

The position variation of the oxygen atom is given by :

At t₁ the position is

At t₂ the position is

The time interval Δt=t₂-t1 is

The time that separates the two consecutive positions and is

c) The percentage of the kinetic energy is obtained as follows:

For x=A/3

The kinetic energy is

The kinetic energy represents of the mechanical energy of the total mechanical energy

A 225 g object placed on a frictionless horizontal table and attached to a spring executes a simple harmonic motion. The spring constant is 125 N/m. The maximum measured displacement from the position of equilibrium is 8 cm. What is the total mechanical energy of the spring object system?