Lab 9

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Temple University *

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1021

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Mechanical Engineering

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Jan 9, 2024

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Uploaded by ProfessorSnow18399

Lab 9: Simple Harmonic Motion Goals: The purpose of this experiment is to learn about frequency, amplitude, period, and what they are about. After learning about the words, we learn how to obtain these factors from the graphs of sinusoidal motion. We are also learning about the type of force that can generate periodic motion. We can then learn about practicing comparing theoretical prediction and experimental results and making the necessary changes, corrections, to the theoretical model. The final note is that we will be adding the knowledge about using the capstone interface, which is a continuously growing learning topic. Apparatus: Coil spring, force sensor, motion sensor, platform balance and stand, Pasco interface, set of masses with hanger. Procedure: 1. Set up the spring sensor, motion sensor, force sensor, and the hanging mass. Then connect the force sensor to the Capstone. 2. Obtain and record the masses of the spring, the weights you would be using, and the hanger. 3. Make sure to set the force sensor to +/- 10 N, on the Capstone computer program. 4. Always make sure to zero, or reset, the force sensor to obtain an accurate reading, before putting the spring and the sensor on it. 5. Make sure to hang the spring from the force sensor 6. Then hang 100 g from the hanger onto the spring, then start the spring very cautiously so that it goes up and down. Then you will record the motion for 3 runs on Capstone and then create a position vs time graph. 7. When you obtain your data, record and last and final run for 150 g and then 200 g apiece. 8. Finally, create a Distance vs Time data graph for a sine function using a fit tool at the top of the graph. Error and Precautions There are multiple errors and precautions that must be considered to have the most accurate results. There are calibration problems that need to be considered of. It is important that every piece of technology used is zeroed, or that the Hz is set to the right number. Temperature also plays a big role in spring. It is important to keep the temperature at a constant for the spring to have a constant stiffness throughout the experiment. Finally, there is human error that must be taken into consideration. When applying pressure to the spring, the pressure applied varies. It must be taken into consideration when looking at the results. By keeping everything constant, it will give the most accurate results. The first three lab results were done incorrectly so our results will not show the real values. Instead of letting it bounce consistently for the first three trials we had reset it every time we started a new trial. This quickly changed when we began working on the 150G and 200G weights as they show accurate results of clear decrease. Results:

Mass of the Spring: 160.3 g Spring Constant: 9.6 N Mass of the hanger: 50 g Force of the hanger: 2.1 N Force of the hanger+100g: 3.1 N

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Questions Question 1. Look again at Hooke’s Law (Eqn. 1). What does the slope of the graph of F vs. x represent?

The slope of the graph represents the spring constant or the stiffness of the spring. Question 2. When you toggle from one run to the next you will notice the position trace may shift to the left or right. Why does this occur? The change in the position trace can be due to more weight added to the spring, the spring losing its elasticity, or the spring's stiffness. It can also be due to adding different pressure when the spring is pressed by one of the students. Question 3. Toggle between your runs. Do you notice a decrease of the amplitude among the three runs? When left to oscillate, the amplitude will slowly decrease over time. Explain why this might occur. I noticed that the very first run had the largest amplitude out of all of the runs. As we progressed through the runs, the amplitude declined each time due to the friction force present. Question 4. Is the frequency about the same for your three runs? Present them on a table for your report. The frequency for all of the trails were relatively similar or the same. All of the trials with 100 g had the same frequency. With 150 g, the frequency decreased a little. Finally, the 200 g frequency declined a bit more from the 150 g, but overall, the three stayed closely similar. Question 5. What change, if any do you expect in the frequency of vibration if we increase the mass in the spring? Hint: see Equation 2 The frequency is inversely proportional to the square root of the mass so if the mass increases the frequency of vibration will decrease and vice versa. A larger mass will need more force to accelerate and will oscillate slower than a lighter mass in the same system. Question 6. Our results support the idea that an object’s natural vibration frequency depends on properties intrinsic to the system itself (like k and m) but is independent of the external force the creates the vibration in the first place. Based on this fact, how does the natural frequency of vibration of a 1 m^3 block of lead compared to that of 1 m^3 block of aluminum? Assume the atoms are a lattice connected by springs (shown at right), and that the stiffness of the bonds between neighboring atoms is the same for aluminum as for lead. Hint: look at the relative masses of these two elements on the periodic table. The stiffness of the bonds between the atoms is represented by the spring constant. Assuming that the stiffness of the bonds is the same for both materials, the only thing important is the mass. The mass would be the atomic unit in the vibration. Lead has a higher mass compared to aluminum meaning that the total mass of the lead block is higher than that of the aluminum block. Since the frequency is inversely proportional to the square root of the mass, the vibration of the lead block would be lower

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compared to that of the aluminum block. The lead block would vibrate less than that of the aluminum block. Discussion: When we began the trials, we had expected the spring constant to be just the average recorded force on the mass hanger until we got help from the lab coordinator who demonstrated that for us to get the spring constant, we needed to get the slope of force vs position on the graph. The first three trials done was believed to have been done in confidence, but it was quickly proven wrong after going deeper into the lab project as the last steps for recording the results of 150G and 200G began to specifically point out their graphs is supposed to be declining over time from the 10 seconds intervals we was recording in the graphs but instead of letting the weights continuously bounce up and down as we recorded the trial we had reset it back in place every 10 seconds and recorded it right after making our decline not noticeable in the 100G results but noticeable only in the 150G and 200G results. The position sensor may have given off a few inaccurate results because it wasn’t perfectly dead center of the force sensor. From what we can include from this lab project is that the frequency will decrease over time as proven by the 150G and 200G lab results.