All the data is provided to you in tables 1 and 2. Solve for table three with the data provided to you in tables 1 and 2 (graphs are also provided for you). Answer questions #1-4 and the questions under table 3, please.

X y 0.0487 -0.19 0.0750 -0.31 0.1970 -0.64 0 0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 -0.1 -0.2 0.0487, -0.19 -0.3 0.0750, -0.31 Force (N) -0.4 y=-2.932x - 0.0666 -0.5 -0.6 0.1970, -0.64 -0.7 Stretch (m)cycles are displayed. See Figure 6. Data Section Again, make sure that the position and Record data in Tables 1 and 2. velocity graph time axes are locked together so that they are aligned. Print Slope of linear fit, k -2.932 N/m out the graph in landscape mode. NOTE: Table 1 Turn off the Smart Tool before printing, as it can interfere with printing. Time at peak #1 2.2 Time at peak #11 10.995 S 0.60 Position, Cat 8 2 R.n "1 Table 2 0.55 Calculation Section Always use un-rounded numbers for all calculations. Average period Period from k and m S Percent Discrepancy % Figure 6 Table 3 6 Use the spring constant (the slope in When the absolute value of the velocity is Table 1), and the known hanging mass of greatest, theoretically where should the mass 0.070 kg to calculate the theoretically be relative to the equilibrium position? expected period and record in Table 3 to three significant figures. 7 Find the percent discrepancy between the measured average period and the theoretically predicted period and record in Table 3 to the correct number of Examining the graph of position and significant figures. Use the theoretical velocity versus time with one to two cycles, period as the "accepted" value. where is the mass relative to the equilibrium position when the absolute value of the 8 Answer the questions listed after Table 3. velocity is the greatest? Turn in this page, a page with your calculations, your three printed graphs, and your printed Force versus Stretch table when Lab HM is due.2 Plug the power supply into the 6 Press the TARE button on the Force Science Workshop interface box and turn Sensor to zero the Force Sensor. it on. Then boot up the computer. 7 Press 'Preview' to start data recording. The 3 Connect the DIN plug of the Force program will begin sampling. Sensor to Analog Channel A. Enter 0.000 in units of meters (m) because the spring is unstretched. Click 4 Click the 'Table & Graph" icon. the 'Keep sample' button to go to the next line. (a) Table 8 Then hang the 10 gram mass hanger from i. In the x-coordinate column, click the Force Sensor, and add a 10 gram "Select Measurement' mass to it, for a total of 20 grams. ii. Click 'Create New' then 'User-Entered Data' 9 Measure the new position of the end of the spring. Enter the difference between iii. Label the highlighted term 'User Data' the new position and the unstretched as 'Stretch' iv. Hit Enter, then label the highlighted term position as the Ax, 'Stretch' (in meters), 'Units' as 'm' for meters. and record a Force value for this Stretch value by clicking on "Keep". v. In the y-coordinate column, click "Select Measurement' 10 Remove the 10 gram mass, and add a 20 vi. Click 'Force' gram mass to the hanger for a total of 30 (b) Graph grams. Measure the new position of the end of the spring, enter the stretch value i. For the y-axis, click 'Select Measurement' ii. Click 'Force', this will provide a Force and click 'Keep Sample' to record the force value. vs. stretch graph At the bottom of the screen, change 11 Continue to add mass in 10 gram increments until the total mass (including hanger) is 70 grams. Each time you add Continuous Mode Camp Made mass, measure and enter the new displacement value from equilibrium. 5 Temporarily remove the 10 gram mass click 'Keep Sample' in Capstone to record the force value. hanger from the end of the spring. Use the meter stick to measure the position of 12 In Capstone, stop data recording by the bottom end of the spring (without any clicking on the Stop button. mass added to the spring). Write this measurement down on a scrap of paper, 13 Rescale the Graph axes to fit the data. and then measure other positions relative Select the data points, but DO NOT to this measurement. That way, you will SELECT the point 0,0. Once highlighted be measuring the stretch in the spring. autoscale the graph ( :> ).Sensor's stereo phone plugs into Digital Channels 1 and 2 of the interface. Plug Next, click the 'Fit' menu button () the yellow-banded (pulse) plug into Select 'Linear'. (NOTE: Don't use the Digital Channel 1 and the second plug point 0,0, since the spring isn't truly (echo) into Digital Channel 2. relaxed at this position because of its design.) 2 Open a position vs. time graph and a velocity vs. time graph in Capstone. 3 Remove the Force Sensor and suspend the spring so that it can move freely up am and down. Put a 50 gram mass hanger on the end of the spring. Add a 20 gram mass to the hanger for a total of 70 Figure 3 grams. 14 Record the slope of the linear fit in Table I in the Data section. It is the spring constant, k. 15 Print out both the table and graph of force versus Ax. Make sure that the value of the slope is visible in the Linear Fit box printed in the table on the graph. Note: you will have to drag the right side of the box containing the slope in order to make all of the slope digits visible when printing. (They might be visible on the screen, but will cut off when printing.) See Figure 3. For the graph, it may be more appropriate to print it in landscape rather than portrait mode - see the print setup menu item. Procedure - Part II - Setup and Figure 4 measurement of SHM 1 Disconnect the Force Sensor's DIN plug 4 Place the Motion Sensor on the floor from the interface. Connect the Motion directly beneath the mass hanger. SeeFigure 4. Adjust it so that the motion out the graph of position versus time and sensor is "looking" directly upward at the velocity versus time. Landscape mode is hanging mass. Set the switch setting on probably better than portrait mode for the Motion Sensor to NARROW. printing. 5 Adjust the position of the spring so that the minimum distance from the mass hanger to the Motion Sensor is greater than the Motion Sensor's minimum distance (15 cm) at the maximum stretch of the spring as it bounces up and down. 6 Pull the mass down to stretch the spring about 20 cm. Release the mass. Let it oscillate a few times so that the mass hanger moves up and down without any Figure 5 side to side motion. 2 Use the Capstone Coordinates Tool 7 Press Start in Capstone. The plots of to measure the period of oscillation. Move the position and velocity of the the tool to the Ist peak in the plot oscillating mass will be displayed. of position versus time and read the Continue recording for about 15 seconds. value of time. Record the value of time in Table 2 in the Data section. You should actually move the coordinate cursor above 8 Click Stop to stop recording data. The the top of the peak, since if you place it on position curve should resemble the plot the peak, it only "stops" at the actual of a sine or cosine function. See Figure 5. data points, which might not be at the If it does not, or if there are "glitches" or very top of the peak. "spikes" in the data, adjust the alignment of the Motion Sensor and the bottom of 3 Next go to the 11" peak in the plot, and the mass hanger at the end of the spring. use the Smart Tool to measure the time, If you need to collect new data, make and record in Table 2. sure that you remove all Data runs before starting over. 4 These two measurements are ten periods of oscillation apart. Take the difference Procedure - Part III - Analysis between these two measurements, divide by ten, and record as the average period 1 Rescale ( ) ) the graph data so that in Table 3 to three significant figures. the interval of interest of 15 seconds is displayed. Lock the two time axes 5 Then, Drag the numbers on the together so that they are aligned. Print horizontal axis until only one to twoSHM--LAB #10 Addendum 1.)What were the initial conditions (x, and v) when this graph began (motion started by you)? 2.) At what time does the mass hit it's maximum position initially? 3.) Calculate what the position and velocity would be at t=30 seconds. 4.) Was energy conserved? Explain why or why not Simple Harmonic Motion Solving this equation gives Equipment Needed x = x,, cos(wt + () Power supply for Science Workshop in which interface Force Sensor (CI-6537) k Motion Sensor (CI-6742) ( = = 2nf =- m T 10 and 50 gram mass hangers Table clamp and right angle clamp So the period of the SHM is given by Spring. k of 2 to 4 N/m, (632-04978) Meter stick Short post and hanger hook m T = 2n Two 10 and one 20 gram masses k Purpose Procedure - Part I - Setup and spring constant In this experiment you will measure the simple harmonic motion (SHM) of a mass 1 Using a support rod and clamp, suspend on a spring. First, by applying known forces to the spring, and measuring its stretch, you the spring from the Force Sensor's hook will measure the spring constant, k, of the so that it hangs vertically. Put a 10 gram mass hanger on the end of the spring. See spring. Then, you will hang a mass on the end of the spring, and set it into SHM, and Figure 1. measure the motion with a motion sensor. You will compare the measured period to the theoretical period. Theory The force that a spring exerts on a mass at position x is given by F = -kx The equation relating force and acceleration is d' x F = -kx = ma = m Figure 1 dt 23 2.5 X Run #1 Run #1 2 2.0 1 1.5 0 MWWWWWW 10.99 s, 0.42 m 2.200 s, 0.315 m 1.0 1 A Velocity (m/s) A Position (m) -2 O -3 0.0 3.92 s, 0.61 m -4 0.5 -5 -1.0 -6 -1.5 -1- [m=?] 2 4 6 8 10 12 14 16 18 2 3 5 6 7 8 9 10 11 12 Time (s) Time (s) [Graph title here ] [Graph title here] O O