216 Lab 6

LAB 6: HARMONIC MOTION Brendon Beckendorff Texas A&M University College Station, TX 77843, US. Abstract This lab is dealing with harmonic motion and the ability to determine a spring constant for different springs. Simple harmonic motion is a type of periodic motion in which the acceleration of the object is proportional to the distance from the fixed point. For this experiment, we will be testing the spring constant for three different springs with different masses hanging from them. We should be able to do this by finding the period of the waves on the graph of function versus time. With this, we can plug in the period into an equation to find our constants. These springs will have a restoring force given by Hooke’s Law. This law states that the deformation of an elastic object will be proportional to the stress applied to it. Keywords: Harmonic Motion, Constant, Period, Hooke’s Law, Elastic 1. Introduction The main concept expressed in this lab is Hooke’s Law. This law involves the theory that elastic objects that have stress applied to them will have an equal deformation as a result. Another concept involved in this lab is how as a spring constant increases, the period of that spring will decrease and vice versa. This is due to the variety of stiffnesses that can be found in springs. With these concepts in mind, our goal for this experiment is to find that spring constant for three different springs with one of them having a different applied force than the other two. Time = Timestamp / 1000 Equation 1 This will be used to convert the timestamps we were given into seconds which is a SI unit. Period = 2 π ( √ ( Length Gravity ) ) Equation 2 This is the formula for period but we will find ours based off the graphs of time versus position. F =− kx Equation 3 This is Hooke’s Law for determining the spring constant. Period = 2 π ( √ ( mass k ) ) Equation 4 This formula will be used after we find the period from the graphs to find our constant. 2. Experimental Procedure This experiment’s goal is to determine the spring constants of three different stiffnesses of spring. To do this, we use the same tracking camera and dots used for all the previous labs. For this lab, we will hang a spring from a metal rod from above and then attach a varying weight to the bottom. Then, we will slowly pull down the weight then release it causing the spring to oscillate and giving us various position points. We will then graph these position points versus time to find the period of each wave on the graph. With this period of oscillation, we will plug it into an equation shown above to find our spring constants for all three springs. Along with this data, we will use standard deviation on our ranges of data to determine the uncertainties.

3: Results and Analysis 0 2 4 6 8 10 12 14 16 18 0 100 200 300 400 500 600 Time vs Position Green X Position Y Position Time (s) Position (pixels) Figure 1: Time vs Position Green 0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 Time vs Position Red X Position Y Position Time (s) Position (pixels) Figure 2 Time vs Position Red