A particle moves in one dimension (along the x-axis), where the potential energy is given by the function U(x) shown below. The constants are A = 2.00 J/m2 and B = 4.00 J/m. The total energy of the particle is E = 8.00 J. U(x)= Ax2+Bx A) What is the equilibrium position of the particle (x, in units of meters)? Is the equilibrium position stable or unstable?  B) What range of positions is the particle restricted to? Give both xmin (the smallest possible position) and xmax (the largest possible position), in units of meters. Hint: the particle is restricted to move in the region where E ≥ U(x).

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Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest.