# 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/s2, 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.