In physics the terms of mechanical energy usually refers to Potential energy (U) and Kinetic Energy (K). In the absence of non-conservative, or dissipative forces, these energies obey the law of conservation of energy, or ΔU + ΔK = 0. That is, when a system is only acting under the influence of conservative forces its total energy content never changes, the energy just converts between forms.
At any point in the cycle, the total energy is constant, U + K = Umax = Kmax. Remember our two relationships involving work
The work done by a conservative force decreases an object's potential energy while it is increasing its kinetic energy
Defining the initial potential energy Uo = 0, gives us
Using the calculus, we see that our desired expression of the instantaneous restoring force being equal to the negative derivative of the potential energy function.
See also this Potential Energy diagram.
The curve represents the value of potential energy U as a function of the particle's coordinate x. The horizontal line above the curve represents the constant value of the total energy of the particle E. The total energy E is the sum of kinetic ( K) and potential ( U) energies of the particle. ( U <= E)
In the slope of zero, F=0, is said to be the state of equilibrium. This terms means the net force act on the object is zero and initially There are two kinds of equilibrium: * Stable equilibrium means that small deviations from the equilibrium point create a net force that accelerates the particle back toward the equilibrium point (think of a ball rolling between two hills). * Unstable equilibrium means that small deviations from the equilibrium point create a net force that accelerates the particle further away from the equilibrium point (think of a ball on top of a hill) * Neutral equilibrium occur when the force is zero for some distance. If it is displaced to one side the force is still zero