Simple Harmonic Motion

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School

Temple University *

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1021

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Chemistry

Date

Jan 9, 2024

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Uploaded by ProfessorMoleMaster802

Title: Simple Harmonic Motion Group 33: Van Tran, Elyse Gallagher, Shrenik Patel Experiment Date: November 7th, 2023 Goals: The purpose of this lab was to get a better understanding of frequency, period, and learn how to extract them from graphs of sinusoidal motion. We also focus on understanding the kind of force that can generate periodic motion, and practice comparing theoretical predictions and experimental results, as well as make connections to a theoretical model. Procedure: ● Set up the spring, force sensor, motion sensor hanging mass as shown in the figure ● Measure and record the mass of the spring and the mass of the hanger ● Connect the force and motion sensors to the interface, set the switch on the force to measure +/-10 N, create a graph and a table for both distance vs. time and time vs. distance ● Zero the force sensor ● Hang the spring from the force sensor and check that it is working properly by viewing the force readings in Capstone ● Find the spring constant k ● Hang a mass hanger from the spring and add 100g to it ● Collect position vs. time data in Continuous Mode for about 10 seconds ● Stop collection. With the mass still oscillating, collect two more runs ● Test answer to question 5 by collecting runs with 150g and 200g on the hanger Precautions and Sources of Error : Precautions and errors can include human error. For example when determining our graphs we had to do our best judgment. As well as placement of motion sensor was placed in best judgment to get most accurate readings Data:

Trial 1 Trial 2

Trial 3

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Trial 1 with 100g mass

Trial 2 with 100g mass

Trial 3 with 100g mass

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Mass of spring: 160.3 g

Mass of hanger: 50.0 g K constant: 10.3 (determined from slope of graph from position vs force, we took the average of ours since our slope for each was slightly different from one another) Theoretical: f = (1/ )(√k/m) 2 2 Experimental: f = w/ 2 2 Frequency Trial 1: k=10.3 Theoretical: 0.347 Experimental: 1.33 Frequency Trial 2: k=10.6 Theoretical: 0.352 Experimental: 1.42 Frequency Trial 3: k=10 Theoretical: 0.342 Experimental: 1.33 Frequency Trial 1 with 100g k= 9.40 Theoretical: 0.273 Experimental: 1.02 Frequency Trial 2 with 100g k= 9.45 Theoretical: 0.277 Experimental: 1.02 Frequency Trial 3 with 100g k= 9.09 Theoretical: 0.272 Experimental: 1.02 Questions:

Question 1. Look again at Hooke’s Law (Eqn. 1). What does the slope of the graph of F vs. x represent? It represents the spring constant. 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 position depends on the starting point and the oscillation did not start at the same exact point each time therefore a shift can occur. 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. The reason for the decrease is because of the energy lost as the spring oscillated with the hanging mass. So with enough time the mass will return to the equilibrium of the SHM. Question 4. Is the frequency about the same for your three runs? Present them in a table for your report. Trial 1 Data Run 1 Run 2 Run 3 Frequency 1.33 1.42 1.33 The frequency for all trials are relatively close to one another. The average is 1.36. Question 5. What change, if any do you expect in the frequency of vibration if we increase the mass on the spring? Hint: see Equation 2. If you increase the mass, the frequency will be smaller based off equation 2 and we can see that when we added 100g to our spring in our experiment that the frequency decreases. 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 m3 block of lead compare to that for 1 m3 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 two would be very similar but the lead is greater in density and mass which would result in a smaller/lesser frequency than the aluminum block. Atoms closer together result in a smaller distance between them.

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Discussion: In today's lab we learned how to determine frequency and period from the graphs of sinusoidal motion. As well as we focused on understanding the kind of force that can generate periodic motion, and practice comparing theoretical predictions and experimental results, as well as make connections to a theoretical model. We were able to determine our frequency by using force vs position and position vs time graphs. The k constant was determined from the slope of the force vs time graph. We found our spring constant to be relatively the same for all three trials. From there we could determine our frequency by using both graphs and the below equations Theoretical: f = (1/ )(√k/m) 2 2 Experimental: f = w/ 2 2 Our experimental frequency for all three trials were relatively close and found that the average was around 1.36 Hz. When we added more mass to the system our frequency was smaller than that without the added mass. We found that when you increase the mass of an oscillator the frequency gets smaller while the period got larger. Errors in our experiment include human error where we had to use best judgment for the motion sensor as well as best judgment when analyzing our graphs.