Simple Harmonic Motion

You can check that equation 63 is correct by

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Unformatted text preview: is correct by substituting equations (61) and (62) into it, and then separating out the x, y, and z components. Figure 10 Center of mass of a generalized system of two particles 3.0 References • • • • Fundamentals of Physics Extended 7th edition by Halliday, Resnick, and Walker. Wiley Publishing Physics 3rd edition by James S. Walker. Prentice Hall Publishing Schaum’s Outline of College Physics 10th edition by Frederick J. Bueche and Eugene Hecht. McGraw Hill Publishing Essentials of College Physics by Serway and Vuille. Brookscole publishing 11 4.0 The Experiment 4.1 Mass and Spring The first part of the experiment that you will perform today, will deal with an oscillating cart on a frictionless air track with two springs attached to it. Thus because we are dealing with a mass that is attached to springs, it is useful start with Hooke’s law. (64) where Fs is the force due to the spring, k is the spring constant, and x is the displacement. The first way that you will measure/calculate the spring constant is by measuring the displacement of a mass caused by the force of gravity. Therefore we can write the spring constant as || (65) where m is the mass of the object, g is the acceleration of gravity, and x is the displacement caused by the object. Another way that we can find the spring constant is by oscillating the object and measuring its frequency. Thus we know that 2 4 (66) Now that we know how to find the spring constant, we will find the frequency of an oscillation mass in two ways. The first way we will do it is by looking at the situation when a mass is attached to a spring. When a mass is displaced from its equilibrium position, it will oscillate sinusoidally about that equilibrium position. If there is no dissipative forces (friction), the displacement x, is given by cos 2 (67) where xm will be how far you displace the mass (cart in this case), f is the frequency (of the fit given by DataStudio) of the motion measured in Hz and t is the total time of 10 oscillations measured in seconds. The second way that will we mea...
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