Physics 4 al experiment 3

# Physics 4 al experiment 3 - Physics 4AL Lab for Science and...

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Physics 4AL Lab for Science and Engineering Mechanics Experiment 5: Simple and Damped Harmonic Motion Lab Section: 8 Name: Christine Probst UID: 303458589 Date: February 21, 2008 TA: Yong WANG Partner: Jimmy Wang Lab Station: 9

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Introduction Simple harmonic motion (SHM) is the motion of a simple harmonic oscillator that is neither driven nor damped. SHM is a very useful way to explain many physical phenomenons throughout the universe. The very foundation of physics, quantum theory, rests on the belief that electrons and other subatomic particles behave as waves. Therefore, it is of utmost importance to understand the behavior of waves in a quantitative manner. The goal of this experiment is to calculate some basic components of a wave in simple and damped harmonic motion. This experiment uses a spring and a force transducer to calculate the period and frequency of damped and undamped systems. Equations F=-kx Hooke's Law F= force (N) K=spring constant (Nm) X=distance displaced from equilibrium (m) Mx''=-bx'-kx The motion of mass under damping X= Position (m) M=mass(kg) B=damping due to magnetic resistance K=spring constant (Nm) Q=(km)^½/b The Quality factor M=mass (kg) B=damping due to magnetic resistance K=spring constant (Nm) W=(k/m)^.5 W is the frequency of a free oscillating mass W=frequency (1/s) K=spring constant M=mass (kg) W o =W free (1-1/(4Q²))^½ W o is the frequency in damped harmonic motion Q=pi/2ln(Rn) Calculate Quality factor experimentally Rn=ratio of peaks Rn=A 2 /A 1 Ratio of peaks calculated from amplitudes Procedure First, measure the spring constant k by weighing a series of five small masses as well as a zero mass and record the change in position. Then, using excel, graph Force vs. change in equilibrium. The spring constant is the slope of this line, which can be recorded by adding a trend line. Knowing the spring constant, the next step is to create a system undergoing simple harmonic motion and measure its frequency. Attach the spring to a firmly secured force transducer (FT) and make sure it can move freely. The coils of the spring should not touch at any point during its natural movement. Next, hang a known mass from the spring, and, again make sure the coils do not touch during normal motion. Don't forget to weigh the spring an include 1/3 of its total weigh as a mass additive. Now raise the weight vertically a few centimeters from equilibrium and release, while simultaneously instructing PSW to begin reading FT data. After an interval of 20
seconds, stop data recording and transfer the output to excel for further analysis. Plot the data on excel and observe the peaks. Calculate the period and the angular frequency of

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## This note was uploaded on 07/02/2008 for the course PHYS 4AL taught by Professor Slater during the Spring '08 term at UCLA.

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Physics 4 al experiment 3 - Physics 4AL Lab for Science and...

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