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# LAB 5 - Physics 4AL Lab for Science and Engineering...

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Physics 4AL Lab for Science and Engineering Mechanics Experiment 5: Simple and Damped Harmonic Motion Lab Section: LAB 5 Name: Sun-Yi Lim UID: 503576474 Date: 7/20/10 TA: Chris Tyndall Partner: Jaimie Yap

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Introduction & Purpose The purpose of this experiment is to analyze a simple spring system and verify relationships such as Hook’s Law, simple harmonic motion, and damped harmonic motion. The setup consists of a spring, mass, string, and force transducer. The force transducer is used to make an indirect measurement of the position of the mass as a function of time. After the value of the spring constant is found though Hooke’s Law, the period of oscillation and relative peak to peak amplitudes will be analyzed. Hooke’s Law states that: =- F kx We will calculate the period, amplitude, and frequency of both simple harmonic motion and damped harmonic motion. We will also calculate Q, or the quality factor, of damped harmonic motion. Theory & Equations Using the basic equation from the Hooke’s Law, which states that: = - F kx Where F is force (N), x being the displacement (in meters) and k , which is the spring constant. The spring constant is obtained by plotting force vs. displacement graph. Regression is performed to determine the slope (the spring constant) and the uncertainty. Once the appropriate voltage is obtained using the transducer and the spring, we will measure at least five oscillations to calculate the amplitude: = + - An Vn 1 Vn Where A is amplitude, + Vn 1 is the local maximum voltage, and Vn is the local minimum voltage. Using the amplitude calculated, the amplitude ratio ( Rn ) will be calculated to find the quality of each type of the motion: = + Rn An 1An At least 5 R’s should be calculated to obtain a good average value for Q. Each Q can be calculated and averaged out in following fashion: =- Qn π2∙lnRn = = Q 1Nn 1NQn Where, N is the number of Qn that we have obtained.
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