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Simple harmonic motion occurs when a constant mass is subjected to a linear restoring force. The angular frequency of the simple harmonic motion is omega = sqrt(k / m). This is the most fundamental thing you need to know about simple harmonic motion. The second thing is to understand that simple harmonic motion of amplitude A and angular frequency omeaga can be modeled by a point moving around a reference circle of radius A at angular velocity omega. At each clock time t that point has a radial vector r, a velocity vector v and a centripetal acceleration vector a. If each of these vectors is respectively projected on the x axis (i.e., just multiply the magnitude of the vector by the cosine of its angle with the x direction) the result is the position, velocity and acceleration of the simple harmonic oscillator at that clock time. (It is also possible to project the vectors onto the y axis to get a alternative model; in fact the vectors can be projected onto any straight line through the origin to get a valid model for simple harmonic motion with amplitude A and angular frequency omega).

Remember that the force constant k for a rubber band chain is the slope of the tension force vs. length graph. For a rubber band chain the graph won't really be linear, but for a small range of motion in the vicinity of some equilibrium point it will be nearly linear, and k will be taken as the slope of the best-fit line.

Hang a known weight from a rubber band chain and let it oscillate gently while you count oscillations for 30 seconds (if you don't have anything of known weight, use a measured amount of water in a suspended plastic bag (if you fill a soft drink container with water, then divide the contents in half, the amount should be about right).

Figure out the angular frequency (omega) of the oscillations and use the angular frequency, along with the mass of the hanging weight, to determine the force constant k.

Verify the force constant k directly by again suspending the original weight at its equilibrium position. Add a known weight equal to to the suspended weight, with the additional weight of roughly 1/10 to 1/4 of the original weight and see how far the system now hangs below the previous equilbrium position. See if your result is consistent with your previously calculated value of k.