Simple Harmonic Motion Experiment

Simple Harmonic Motion ExperimentKisal JayakodyTechnical ReportIn this experiment, a motion demodulator is used to measure the position of an oscillating mass as a function of sentence. The frequency of oscillations will be obtained by measuring the f number and acceleration of the oscillations, and fitting the data to a sine function. The dependence of oscillation period on the mass applied and on the derail constant will be studied.IntroductionAn object oscillating in simple harmonic motion is described by(1)wherey = outdistance from the equilibrium position at time tA = amplitude = maximum distance from equilibrium positionf = frequency = number of oscillations per mho. An oscillation is one complete back-and-forth motion = angulate frequency of the oscillation = 2f = initial form angleT = The period of the oscillation, . = the velocity of the mass = . = the acceleration of the mass = .TheoryWhen a mass hangs from a (massless) spring and oscillates vertically, its period i swhere (2)m = mass hanging from springk = spring constant (k = force/elongation)Squaring both sides,If the springs mass is not negligible this becomes (for a uniform spring),which base be written.(3)For a particular spring, this relation of period squared to mass can be written as a declinear equationwhere and x = mass.So a graph of T2 versus mass should be a straight line withSlope = (4)Intercept = (5)Pre lab assignmentFind the period and the frequency of an object that oscillates 30 times in 44 seconds.2. In the sample graph, go up the value of each of the following 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 sensorSpring, 6 cm by 1.5 cm from Pasco track acc essoriesLarge table clamp, right angle clamp, multi-position pendulum clamp and rods to hold spring and motion sensor (see Figure 1)50 g mass holder50 grams of masses (110 gram and 220 gram masses)MeterstickProcedure and Analysis for the Simple Harmonic Motion ExperimentI.Set-up of computer and portholeTurn on the Pasco 750 interface first. Notice that the indicator light is on.Turn on the computer and login.Set up the equipment, as shown in Figure 1Click on Data Studio, following separate Data Studio instructions.Select Motion sensing element.Double click on Motion to get to Sensor Properties.Under Motion Sensor, increase trigger rate to 25 Hz.Under Measurement, make position, and leave velocity and acceleration as selected.Click and drag velocity from the Data Window, to the graph icon to create 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 lock 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 fish holder from the spring, as shown in Figure 1.switch on the sensor for narrow beam and link 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, chew up or lower the rod holding thespring until the bottom of the weight holder is about 40 centimeters above 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 START to begin learning. After a minimum of 5 oscillations, click STOP.VI.Determining the oscill ation frequency by a sinusoidal fitClick on Zoom to select the data to be fit. Go to Fit, and select Sine 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 included with your laboratory report.5. increment 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. Finally, disassemble the apparatus and measure the mass of the spring on a balance.VII.Calculatio nsEQUATIONS-09/20/161