Physics finding mechanical energy

Question

An object that follows Hooke’s Law is hanging 2 m above the ground with a mass of 1.5 kg and a spring constant of 1.2 N/m. If the object is at rest when stretched 0.25 m, what is its total mechanical energy? 

Answer 1

The total mechanical energy of a system is the kinectic (moving) and potential (at rest)

E=K+PE

In this case, since it states the object is at rest while being stretched (displaced) that means the total mechanic energy is all potential

E=0+PE or E=PE

and PE=(1/2)(k)(x^2)

where k is the spring constant and x is the displacement from equilibrium. In the case of a spring system, the mass of the object and it's distance above ground are irrelevant. Since the spring has not been release and is being held at rest we will use only PE to calculate our answer. Keep in mind that Energy need to be in Joules (J) and J=N*m.

PE=(1/2)(1.2N/m)(0.25m)^2

=(1/2)(1.2)(0.25^2)(N/m)(m^2)

=(0.5)(1.2)(0.25^2)N*m or J