Suppose you are an engineer for a motorcycle manufacturer. You are assigned to the team designing the motorcycle's rear suspension. You are studying the properties of springs that are strained horizontally. Your experimental setup is animated in the simulation (linked below). In this simulation, a particle is given an initial velocity at x = 0, and it moves in the + x direction while slowing down due to the elastic force. When the block is at x = 0, the spring is unstrained, and therefore exerts no force on the block. So x = 0 is the particle's equilibrium location. The end of the interval is taken to be at the one-meter mark, which is where the particle is momentarily at rest. That is, x₂ = 1 m. Run the animation now. Simulation The Elastic Force Acts on a Moving Block The simulation shows the true spring force on the block as it moves (see the solid blue arrow labeled "Exact Force"), and it also shows an approximation to the exact force (see the dashed blue arrow labeled "Approximate Force"). Note the behavior of the approximate force. It jumps discontinuously to a new value each time the block completes a displacement of size Ax = x₂/N. Both the true and the approximate forces are plotted in the simulation above the animated motion. The area between the plot of the approximate force and the x-axis is a series of narrow rectangles shaded in light blue in the simulation. The exact force is the line Fx = kx, which is shown in green in the plot.

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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.