Simple Harmonic Motion Experiment

open Harmonic Motion tasteKisal JayakodyTechnical ReportIn this experiment, a exploit sensor is used to measure the position of an hesitate plentitude as a function of time. The frequence of tremblings bequeath be obtained by measuring the swiftness and acceleration of the oscillations, and fitting the data to a hell function. The dependence of oscillation period on the portion applied and on the re piece of tailt constant will be studied.IntroductionAn object oscillating in simple harmonic motility is described by(1)wherey = distance from the equilibrium position at time tA = amplitude = utmost distance from equilibrium positionf = relative frequency = number of oscillations per second. An oscillation is one complete back-and-forth motion = angular frequency of the oscillation = 2f = initial phase runT = The period of the oscillation, . = the velocity of the mass = . = the acceleration of the mass = .TheoryWhen a mass hangs from a (massless) take a hop and oscillate s vertically, its period iswhere (2)m = mass break from rallyk = jump-start constant (k = force/elongation)Squaring both sides,If the springs mass is not negligible this becomes (for a uni fix spring),which can be written.(3)For a particular spring, this relation of period square to mass can be written as a analogue equationwhere and x = mass.So a graphical book of account of T2 versus mass should be a straight line withSlope = (4)Intercept = (5)Pre lab identificationFind the period and the frequency of an object that oscillates 30 times in 44 seconds.2. In the seek graph, find the value of each of the hobby quantities make sure you include proper unitsamplitudefrequencymaximum velocitymaximum accelerationinitial phase angle (of position-time graph)3.In the sample graph, at t 0.9 seconds, y = maximum. Explain whyv = 0a = negative maximumAlso, at t 1.2 sec., y is at the midpoint of its oscillation. Explain whyv = negative maximuma = 0ApparatusPasco 750 InterfaceMotion senso rSpring, 6 cm by 1.5 cm from Pasco track accessoriesLarge table clamp, right angle clamp, multi-position pendulum clamp and rods to hold spring and motion sensor (see Figure 1)50 gee mass bearer50 grams of masses (110 gram and 220 gram masses)MeterstickProcedure and Analysis for the Simple Harmonic Motion ExperimentI.Set-up of computer and interfaceTurn on the Pasco 750 interface first. Notice that the exponent light is on.Turn on the computer and login.Set up the equipment, as shown in Figure 1Click on Data Studio, succeeding(a) separate Data Studio instructions.Select Motion Sensor.Double chaffer on Motion to get to Sensor Properties.Under Motion Sensor, add trigger rate to 25 Hz.Under Measurement, select position, and leave velocity and acceleration as selected.Click and line velocity from the Data Window, to the graph icon to bring on a velocity versus time graph.Click and drag acceleration from the Data Window to the bottom of the velocity graph to create an acceleration graph below the velocity graph.Click on the keep mum icon to keep the time axes of the plots locked together.Set-up of equipmentSet-up a desk clamp and rods to hold the spring as in Figure 1. Hang the 50g weight holder from the spring, as shown in Figure 1.switch on the sensor for narrow glitter and connect the yellow plug to digital channel 1 of the Pasco interface, and the other plug to channel 2.V.Recording of position-time data during oscillationsWith just the 50 gram holder on the spring, raise or lower the rod holding thespring until the bottom of the weight holder is roughly 40 centimeters to a higher place the motion sensor. This is done so that the distance from sensor to weight holder will never be less than about 30 centimeters during an oscillation. This is to insure that the motion sensor accurately measures the distance.Start the weight holder oscillating vertically, about 5 centimeters above and below the equilibrium position. Click on first-class honours degre e to begin recording. After a minimum of 5 oscillations, click STOP.VI.Determining the oscillation frequency by a sinusoidal fitClick on Zoom to select the data to be fit. Go to Fit, and select sinning Series Fit. Fit the velocity data, and the acceleration data separately. The data points should form a smooth sine curve. If they dont, delete the data and record data again. To delete the data, click on run1 in the experiment set-up window, hit delete, and click on OK.The fitted curve should match the data.Into a second excel spreadsheet, record the mass on the spring, the amplitude of the velocity, of the acceleration, the frequency of the velocity, and the acceleration.Print out a few representative graphs to be include with your laboratory report.5. Increase the hanging mass to 60g (total) and again adjust the spring support so that the mass hanger is about 50 cm above the motion sensor. Repeat V and VI.6. Repeat the above steps for a total mass of 70, 80, 90, and 100 grams7. Fin ally, disassemble the apparatus and measure the mass of the spring on a balance.VII.CalculationsEQUATIONS-09/20/161