where

is the displacement of the end of the spring (x) from its equilibrium position ();

is the restoring force exerted by the material; and

k is the force constant (or spring constant).

The potential energy of a spring can be expressed as

It becomes more complicated when a spring is hang in a vertical direction under gravity g.

If the end of the spring is when there is no mass attached to the spring.

The equilibrium position becomes when a mass m is attached.

The motion is still a Simple Harmonic motion (SHM) if the mass is pushed/pulled away from the equilibrium position and released. What will be the spring force and potential energy look like as a function of y?

I hope the following simulation will help you find out the answer.

There are two tabbed panel in the simulation. One for horizontal spring and another one for vertical spring under gravity.

You can drag it to move the mass away from the equilibrium position, it will show external force and spring force.

The blue vurve is the force as a function of d : or

The red curve is the kinetic energy

The green curve is the spring energy: , where or

The black vurve is the potential energy

The yellow curve is the sum of

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

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