SHM lab

pdf

School

Western University *

*We aren’t endorsed by this school

Course

1202

Subject

Physics

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by nguyenjasmine10

| OTOTOTOTO OO OO0, Simple Harmonic Motion - 5 Data and Work Sheets Simple Harmonic Motion - Physics 1202B 2023-2024 EEE ~ Please circle the appropriate values | b e W Course 1102B 1202B 1402B 1502B P S Lab Section 002 | 003 | 004 | 005 |( 006) 007 | 008 | 009 | 010 | 013 | 014 | Lab Subsection A B w D = T Name Fnrs Last: m Student # i = 2]6]\\68 2 | 6 | Lab Partner First: Last: DO Lab Station # 10 Date Tuesday Janoary 30,2024 Demonstrator lan * Baria Disclaimer: Please note that some but not all questions in this lab writeup will be graded. EXPERIMENT 1: MEASURING THE SPRING CONSTANT OF THE SPRING APPARATUS: steel helical spring, masses, meter ruler and mirror (to eliminate parallax) METHOD You should have a setup as shown in Figure 1. The spring is hung on a force sensor. The force sensor and the ultrasonic device are not used in Experiment | when the spring constant is measured, but will be used in Experiment 2. Record in Table 1 the position of the lower end of the helical spring with no masses attached. This is the equilibrium position, xg, of the spring. Now, add a mass to the spring and record the mass (m) attached to the spring, and the position (x) of the lower end of the spring, in Table 1. (Note that you should always start with the lowest mass so as to not elongate the spring past its breaking point. The displacement (x — xg) should be at least 3 ¢cm and no more than 20 cm. Continue to increase the load on the spring by small increments, by either adding masses or by substituting a heavier mass, and record the position of the lower end of the spring for each mass. Add masses gently so that the spring extends monotonically, i.e., without bouncing the load on the spring. Repeat this process for at least 4 different masses.

Simple Harmonic Motion - 6 Ruler Mirror —Spring _/Mass nannnnnnnnnnnnnnnannn 11J Figure 1: Setup of vertical mass-spring system. The spring is suspended vertically and extended due to the weight of a mass attached to the end. The mirror is used to reduce measurement errors due to parallax. The force and motion sensors are not shown in this schematic, Calculate the corresponding displacement (x — xp) of the spring for each mass, and record (x — xq) in Table 1. The displacement is the increase in length from the equilibrium position of the spring. Include an estimate of uncertainty in the column heading for each variable. Table 1: Static (non-oscillatory) force-displacement data for determining the spring constant of the mass-spring system Mass m (g) Position x (cm) Weight (N) Displacement (x - x() (m) 3 0.4 + 0.08 £ 0.002 £ 0.001 0.0 24.30 0.0 0 3009 23. 60 2.943 0.033 5009 32,35 4.90S 0.0%) 6009 35.10 5.886 0.108 1009 33. 495 6.3 63 0.131 8009 39.90 3.4 0.156

Simple Harmonic Motion EXPERIMENT 1(a): DETERMINATION OF THE SPRING CONSTANT 1. Using Excel, plot weight (in Newtons) versus displacement (x — xp). 2. Fit a straight line without forcing the fitted line through the origin to determine the spring constant k. In Excel, use the “Add Trendline™ function to add a linear line with the display equation option selected. 3. Determine the slope. 9: 39, 6ok + 1. GUL) What is the spring constant? spring constant (k) = Sope of wt\gh\'(kl) s, displacement (m) 5(aph = 30,608 Nlwm EXPERIMENT 2: DETERMINATION OF THE PARAMETERS OF A SIMPLE HARMONIC MOTION In this experiment, you will record the position, velocity, acceleration and force using the ultrasonic position-measurement device and a force sensor. The parameters of the oscillation will be obtained by graphical analysis of data collected by the Logger Pro software on the lab computers. Each group will measure the oscillation of the vertical mass-spring system using the same spring but with two different masses but the same amplitude. Then they change the am- plitude and repeat the experiment for the two different masses chosen. The students will analyze the data each time to investigate the effects of changing the mass as well as changing the amplitude on the motion of the simple harmonic oscillator. EXPERIMENT 2(a): SETUP 7 In this experiment, you will now use the Vernier force and position sensors to acquire data from the oscillation of a mass on a spring, as shown in Figure 2. 1. Ensure that both sensors are connected to the mini Lab Quest data hub, and the hub is con- nected to the computer. (S} Position the ultrasonic sensor directly underneath the spring. There needs to be a minimum of 15 cm between the sensor and the mass on the spring for the sensor to record accurately. 3. Select 10 N range for the force sensor. 4. Select “cart” position for the ultrasonic position sensor.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Simple Harmonic Motion - 11 I R e L Ly, - - e - M MRS ZLL LY L2 RS ¢ A - Time () A . -1 2 - = 3 5 ?Orce 2 SO y 000N |. 4 Position | ! : m ” ~ ) * 4 s Tene is) Figure 4: While the system is still at equilibrium, the baseline data can be acquired to ensure that all values at equilibrium are indeed zeroed. EXPERIMENT 2(c): MEASUREMENTS Once you are satisfied with having the sensors zeroed with the mass hung on the spring (at the equilibrium position), you may start the oscillation by stretching the spring to an amplitude you have chosen. 1. Choose an amplitude and record it below (do not allow the spring to stretch beyond its breaking point of 20 cm). o . Set the mass to oscillate vertically. Wait and observe that it is oscillating vertically, then click on the green button to collect data. If you wished to start over, let the system finish collecting the data before attempting to restart. If you are happy with the oscillation, for example as shown in Figure 5, then save the data. Go into the File menu, and save the data as *.cmbl files. 3. Choose a meaningful file name, and record that into your lab manual. 4. Repeat the above with a different amplitude and save your results. Amplitude 1 = 10.0em + 0 0fem Amplitude 2= S.0tm + 0, 0lew

Simple Harmonic Motion - 12 2 S ANANANAANANNN Y ' Force . ; : ' : I Tave 2y) _0.12N |77 Position || ;Y YYAAAAAAAAAANAS -0.035m|" ™ ; P . Figure 5: An example of force, position, velocity and acceleration data recorded by the force and motion sensors. Change the vertical axes to a range suitable for the oscillations in your experiment. OBSERVATIONS I. Starting with the Position vs. Time graph, identify times when the velocity should be a) zero and b) a maximum, and confirm that on the Velocity vs. Time graph. o) Yelotitg 1 2¢ve when YRt posihon of an obyectis at a maximum ov a mnimym. b) velotiiy 1§ af maximvm when the posihon of an ebyjeet \s n equilibrivm (posrhon 15 at zevd) 2. Starting with the Velocity vs Time graph, identify times when the acceleration should be 2a) zero and b) a maximum, and confirm that on the Acceleration vs. Time graph. a) aceteleradion is 2evd when the veloarty 1s ot 0 maximum or a2 mmmum, b) acceleyafin (5 ol maximum when e Velocty 1S at ey (equlibnum) 3. Are the oscillations in the Force vs. Time graph consistent with the Position, Velocity and Acceleration vs. Time graphs? Explain why. The oSallations m the Forgp v, Time 0Yoph ave consisient oS the othey gY aphs. The Torce | Time greph exevis a pritern of o simvsoidal funtion wmeh 18 4 Similay pattern with ine posthon veloethy and ateel ¢y abron v§ hime 9Yaphy. DATA ANALYSES Export measured data from Logger Pro for data analyses in Excel Under File menu in Logger Pro, go to export, and export using comma separated values (*.csv) format. Open the exported CSV file in Excel. Note: make sure you now save this file as an Excel file format (*.xlsx), otherwise, your plots will not be saved.

Aayt0 YIvd o pwabd PIAIPISUN axp Balp puv 701 Wit 20 SINBA oM} Ay o 1360 - (71303 0h +$09°6%) 1001 % e sttt [30370h - 309715 | ; %0’)0h&1x ‘ ZIKIX*‘)') $09 b¢ 'Y [00] % { "qn“ = TUWINY L ;uaond (%01 UIYIIAm San[eA 0M) ) a1y "20Ud -12)J1p 1wadiad ay1 2indwod pue ‘[ uawadxy ul paurelqo weisuod Juuds ay) yum aredwo)y ¢ 303 0h =¥ -adogs ayy woyy () weisuod Juuds ay) duTULIA( 7 3EL°0 + X$0Q k- =0 22X Ul OISO sns4aA 2240, 10]d ‘7 yudwuadxy Suunp pannboe eiep o) Suisn | ‘uonisod wnuqrnba SIWoly paydlans uaaq sey suuds ay1 1ey moy 01 euonuodoid st uonisod wnuqipnba ay 01 yoeq ssew 2yl Suuq o) Suuds oY1 £q pauaxd 300§ FuLIOISAI AY) 1Y) SN S| XYy — = . ‘ME[ S, 9OOH (Y) uonISOJ SNSIAA () 3210,] 10| :(e)] SISA[euy “sy01d 729x77 woay sivjpwRIed JUILLINA( :] SISATVNY €1 - uonopy swouley 2qdung

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Simple Harmonic Motion - 14 Analysis 1(b): Plot Force (F) versus Acceleration () Newton’s second law, F = ma, tells us that the force exerted on a mass is proportional 1o its acceleration. I. Using the data acquired during Experiment 2, plot Force versus Acceleration in Excel. Y= 0.6012x * 0.0240 2. Determine the effective mass of the system, m,y, from the slope. In addition to the mass that you hung on the spring, this effective mass also accounts for the mass of the spring itself. The effective mass of the system from the slope 18 0.6010kg. This equates § 601.19. The mas used g fal was 6009, ond the Yermaning 119 accaunts foy the MAss 0% the spring. Analysis 1(c): Plot Acceleration (@) versus Position (x) 1. Using the data acquired in Experiment 2, plot Acceleration (a) versus Position (x). Y= -6%330x + 0.0456 . What physical quantity does the slope represent? o The sloge vepresents the negative angular frequency. [-00%] W . Determine the slope. 4= 6F.3%) 2 + 0.0uUS6 The slope 18 -63.3%]. 4. Determine the measured angular frequency, ®. wh: 6} 331vad” [sec? w: g.20vad[sec S The anguiny {vequmcg 1 $.10ved [,

Simple Harmonic Motion - 15 ANALYSIS 2: Kinematics equation of motion: amplitude, angular frequency, ~and phase of the oscillation Using the data collected in Experiment 2, write the displacement of the oscillation as a function of time by doing the following analysis: a) Determine the amplitude, A, of oscillation from the position data using an averaged peak value. Esumate the uncertainty, and explain the basis for your value (i.e., how you came up with that value). To find the omphtude, o mox = 0-03% posihan vs. hime grapn way protted. min = - 0.0 The mox | min valves were then subtvaded A= (0.036-(-0.034)) /2 and divided by 1. The vncevianty 1s - 0.035m BIHI%s B £0.00\m b) Determine the period of oscillation, 7, from the measured angular frequency found in Anal- ysis 1(c). :. The period of osaloilon M= I . 5. 365 seconds 18 T=0.765s — m— w .11 T " ¢) Determine the phase angle, ¢, from your acquired displacement data (using the displacement at time 1 = 0) % (0)=~0.0%001%m X ()= Asm(wtep) -0 030013= 0.035sm (%.21 (0) 4 9) g: swm™ X- 0.0300l'5] 0+ - 1.03yad 0.03% d) Write the displacement as a function of time, Equation (1), in terms of parameters A, 7" and Q. x(1): 0.035swm (.21 - 1.03)

Simple Harmonic Motion - 16 ANALYSIS 3: Relationships involving the angular frequency ® in simple har- monic motio For these steps, use percent difference tests to compare quantities. N a) Compare the angular frequency (@) that you determined in Analysis 1 with ;;,-’5- -, where k is the spring constant and m, ss is the effective mass as measured and determined in Analysis 1(a) and 1(b), respectively. W,: §.210ad s - diffevenee = | 1821 8241 ' x 1007. W,y ?HO.SOKNIM (s.2048.24) /2 0.5011 k9 , = 0.36°). * 9. 1%vadls b) Plot Acceleration (a) versus Position (x) in Excel for the second data set acquired with a different amplitude and determine the angular frequency. Compare the angular frequencies of the oscillations from two different amplitudes. W, §.11vadlS$ | dviferente = \8.1\'?.57‘ x 1007 Wy'»59.%43 (621 5.5 12 , ®Wi* 3.5Fradls = g ¢) From the acquired Velocity vs. Time data, determine an averaged value of the maximum velocity, vy, for the oscillation. Compare this with the theoretical value, as expressed in Equation (2), using the values of A and @ determined in Analysis 1 and 2. Expevimental : Vmax = 0.307ml§ (frowm 9”Ph) A [ o T 1 1007/ » ; Theovehicol : \Ymax= A= 0-035 (8.21) (0.2%3+ 0.30%3) /1 T 0. 2183Im)s = 6.13). ANALYSIS 4: [Optional] Kinetic and potential energies |. Calculate the kinetic and potential energies in the Excel spreadsheet for one set of data col- lected. 2. Plot both kinetic and potential energy versus position (x) on the same graph. 3. Calculate the total energy, and add that to the graph above.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Simple Harmonic Motion - 17 DISCUSSION AND CONCLUSIONS |. You are given a mass and a spring. setup either in a vertical configuration, as in this lab, or horizontally. When we set the mass in motion about its equilibrium position, can it oscillate with more than one frequency? Explain. No, fhe mass connot oscillate with move han one frequency. The fovmuia of frequency 15 defined as f: E‘EJ’% The spring Constant (k) and the wass (m) ate fixed thvoughout oscilation, meantng these valuts do not change. Thevefove . When wass (5 Sebwn mobon about its equilibrivm positien, frequenty 15 Constant and canvof estllate mave then one Trequenty. 2. The frequency of a simple harmonic motion does not depend on its oscillation amplitude. What must then be changing to allow for the larger amplitude of oscillation within the same period? Based on fhe cquation, V:Aw, Wt can mompulate the equation by using W= 21f and f= ‘—JZ ReMYM\g\V\9 thas equahnon, we gt : MNm. v v (N V , — — . = g — |_ K AR (GO Smte velonty (v)' SpYIng tunshvﬂ'[k)‘ ond mass (m) are pfopmf’ﬂ‘“ﬂ\ ) amp\\fude\ Mhese vaviables con IneriaSe fy nevease the amphivde of osallafion. Marks Table Total Mark (Lab report + Pre-lab )

SHM lab

Related Documents