A certain spring is found not to conform to Hooke's law. The force (in newtons) it exerts when stretched a distance x (in meters) is found to have magnitude 40.0x + 46.1x² in the direction opposing the stretch. (a) Compute the work required to stretch the spring from x-0.28 m tox-0.56 m. (b) With one end of the spring fixed, a particle of mass 2.47 kg is attached to the other end of the spring when it is extended by an amount x-0.56 m. If the particle is then released from rest, what is its speed at the instant the stretch in the spring is x-0.28 m? (c) is the force exerted by the spring conservative or nonconservative?

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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.