# Module 4.2: VerticalSpring

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This model shows the behavior of a vertical spring. Note that it is
very similar to one of the fall models, with changes in velocity and
position (or in this case, length). Because this model shows a spring,
rather than an object, the velocity and length are connected by a
variety of terms to model the behavior of a spring. Let's dive in,
shall we?

**Acceleration due to gravity:** -9.81 m/s^{2}, which feeds into...

**Weight:** acceleration due to gravity * mass

**Mass:** Controlled by the Total Mass slider

**Acceleration:** Acceleration is the term that feeds the change in
velocity slider. Acceleration is a product of the total force/mass.

**Total force:**The total force is the weight plus the restoring spring
force. Unlike the Fall models, a spring has a restoring force that
brings it back to equilibrium. (This will be more interesting in the
next model, which shows a bungee jump).

**Spring constant:** The spring constant represents the spring's
stiffness. It is controlled by the Spring Cons slider.

**Weight displacement:** Weight/spring constant

**Unweighted length:** This controls the initial length of the spring in
its natural coiled position. This number comes from the Unweighted
Length slider.

**Restoring spring force:** The restoring spring force is the result of
Hooke's Law. Restoring spring force = -spring constant *
(length-unweighted length). The length - unweighted length is the
spring's displacement.

**Init displacement:** This is the displacement due to stretching or
compressing the spring. In thi model, it is controlled by the initial
displacement slider.

The stock "length" contains the unweighted length + weight
displacement + initial displacement. Length versus time is graphed in
the right panel.

Play around with the sliders for stiffness, mass, length and initial
displacement. Regardless of the settings, the graph should exhibit the
periodic oscillating waves of simple harmonic motion.