BOBOvHdHHHHHH"H"T " v|-Z(x HH@R (,, N `,0 `A ' dPPDJ h (dl@/j\"4PzNm,zNapS IOKCaU/2jk`1H Spreads "x4(|DSETr"$b!!!wz!%uz#S $ 4 5 ! " # $ % & ' ( ) * + :    Y Z      D E   E   A3  4 5 B   + 7 : C             6 = F Z b   P V [ _ t l o              E S     )   R X        "    .            B  H              3  D            z  {       7 : f n 2vT!"@( AtvPhysics 1150 Simple Harmonic Motion Simple Pendulum Introduction: Simple Harmonic Motion (SHM) is an important type of motion. Many diverse systems either execute SHM or can be approximated by SHM. The example of SHM that we will look at today is a Simple Penduluma mass on a string. Terminology: Amplitude (A) is the maximum displacement from the equilibrium position. Period (T) is the time for one complete cycle or one complete oscillation. Frequency (f) is the number of cycles or oscillations in one second. Note that period and frequency are connected by T = 1/f or f = 1/T. Purpose: In this experiment with simple pendula (or pendulums), we want to find if (or how) the period (or frequency) depends upon the amplitude, the mass, or the length of the string. Procedure: Throughout this experiment, measurement of the periodthe time for one oscillationwill be crucial. You may do this in either of two ways. You can measure the period directly with a stop watch. Measuring the time for a single period is difficult because of your own reaction time. If you use a stop watch, measure the time for ten oscillations and divide that time by ten to find the period. If you use Event Timer, be sure to Configure it to measure the time for two passes. You may need to think about that for a moment; during one period (or one oscillation) the pendulum will pass through a photogate two times. Part 1 (amplitude): Measure (and record) the period for five different amplitudes. How does the amplitude affect the period? Keep everything else (esply the length) constant. Part 2 (mass): You have a lightweight, wooden ball attached to a string and a heavier, steel ball attached to the string. Either mass may be used as a pendulum; be sure to keep the same length for the pendula in the two cases. Measure the period for the lightweight, wooden ball used as a pendulum. Then measure the period for the heavier, steel ball. How does the mass affect the period? Part 3 (length): Vary the length (l) of the pendulum and measure the per(iod (T). For each length, measure the period (at least) three times and find the average. As always, look for consistency. If you measure periods of 1.23 s, 1.93 s, and 1.28 s, something is wrong! Find out what is wrong. Measure the period T for (at least) six different values of the length l. Now we want to find the relationship between length and period. The first thing to ask is are they proportional?that is, can we write an equation like T=Kl? where K is some proportionality constant. Go to Graphical Analysis and see if period and length are proportional. What does proportional mean? What will you find in Graphical Analysis if they are proportional? If they are not proportional, then see if you can find some variation that is proportional. Try plotting the period versus thet square of the length; are those two proportional? Try plotting the square of the period versus the length; are those two proportional? How will you know if two variables are proportional? When you find two variables that are proportional, write an equation that describes that proportionality. What is the numerical value of the constant of proportionality? What might that mean physically? Be sure to look at the units of the constant of proportionality Conclusion: Throughout this lab description, there have been questions. Those should be addressed in the Conclusion. The conclusion should explain what you have found about the motion of a simple pendulum. The Conclusion should explain what determines the period of a pendulum (and what does not affect the period). Be sure to include an equation stating your resultsand an explanation of the terms in the equation.ZNDSET.H\"<a6*aDSET .H|``!azaa{6*faDSET.Hl!`0 *`0    DSETT@!!!! v     !SHM/ Pendulum - pZNDSET.H/vfc Z6*ZDSET .H!;~z  w0r*: 6*ZFNTMCUTSDSUMHDNISTYL$@STYLMvLvlv\vdvvv              4               HASH( & $( ( (((( Ó& %x%& %~)%z;%%A( A(O C& L:Qhjazo}BodB CHARv    "   A A C S 3  ^ HASH       P  R CELLv`"HASH   GRPHvhn~cc k F HASHou%q7wN l RULRvD @@@L HASH @@BL LKUP    $NAMEDefault Default SSHeaderBodyFooterFootnoteFootnote Index DFNTM HelveticaGeneva"New Century SchlbkCharcoalETBL@FNTM CUTS DSUM "HDNI BSTYL LETBL.