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Part 1 – Measuring Spring Constant from Displacement For this section, you will determine spring constant or the unknown mass of an object using the equilibrium position of a mass once it is attached to a spring. To complete this section, you will be using the following website: https://phet.colorado.edu/sims/html/masses-and-springs-basics/latest/masses-and-springs- basics_en.html Figure 1 - Home page of the simulation site 1. When you open the simulation, click on the “Stretch” option. 2. Move the slider on the “Spring Strength” for both Springs down to “Small”. Drag a 50 g mass from the lower left-hand corner and attach it to the spring on the right. 3. Check the boxes for “Unstretched Length” and “Resting Position” the simulation will show the relaxed and stretched position of the springs.

4. Drag the ruler from the right-hand side close to the spring on the right so that you can easily measure the displacement of the mass from the relaxed position of the spring (from the upper blue line to the lower green line). Figure 2 – Simulation setup to measure displacement of masses attached to spring 5. Enter the mass (converted to kg) and displacement from the unstretched length (converted to m) in the Table 1 below. 6. Exchange the mass and repeat the process for the 100 g and 250 g masses. 7. Use Eq. 5 from the theory section to determine spring constant, k 8. Use the average of your 3 calculated spring constants for a k value to fill in the rest of the table. 9. Now that you have a spring constant value to work with, repeat the process of measuring displacement with the three unknown masses and fill the values in Table 1. 10. Use Eq. 5 – this time using the displacement and spring constant values to solve for the respective mass values. Input the mass values into Table 1. Table 1: Equilibrium displacement vs. Mass Mass (kg) Displacement (m) Spring constant, k (N/m) 0.05 .16 3.07 0.1 .33 2.97 0.25 .82 2.99 Small Red mass [.092] .30 3.01 Med Blue mass [.101] .33 3.01 Large Green mass [.199] .65 3.01 Average Measured Spring Constant Value: 3.01 N/m

Part 2 – Measuring Spring Constant from Period In this part of the experiment, you will determine the spring constant or unknown mass of an object by measuring the period of motion as the spring oscillates with mass attached. To complete this section, you will click on the “Lab” button at the bottom of the simulation. Figure 3 - Simulation for period vs. spring constant. All settings are shown for lab Part 2 measurements including: Slow motion selected (bottom-right corner), Period Trace selected (Top-right corner), Timer drag from tools box 1. Navigate to the simulator page and select the following options before beginning:  Slow motion (button is in the bottom-right corner of simulation)  Period Trace (option is in top-right corner)  Drag the timer from the box on the right to be near the spring  Grab the 100 g mass and connect it to the spring. If it is not moving, try dragging it downward to pull it so that it begins oscillating.  Use the default “Spring Strength” – do not move this option 2. Run the simulation and use the timer to record 1 full period of motion for the 100 g mass. Slow motion will make this easier than normal speed. 3. Fill the period value in the table. 4. Repeat steps 2-3 with 200 g and 300 g masses by using the slider on the top left of the spring to change the mass. 5. Use Eq. 7 from the theory section to solve for spring constant using the mass and period values you have filled into Table 2 6. Record the average spring constant value below Table 2 and use this value to fill the spring constant column in Table 3. Use Eq. 7 again to solve for “m” and determine the value of the unknown masses in Table 3. Table 2: Determine Spring Constant from Period vs. Mass

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Mass (kg) Period, T (s) Spring Constant, k (N/m) 0.1 0.86 5.38 0.2 1.17 5.78 0.3 2.61 1.74 Average Spring Constant Value: 4.3 Table 3: Determine Mass from Period vs. Spring Constant Mass (kg) Period, T (s) Spring Constant, k (N/m) Small green mass [_0.042__] 0.62 4.3 Med blue mass [_0.24__] 1.48 4.3 Large pink mass [__0.14_] 1.14 4.3 Analysis 1. Looking at Table 1, what can you conclude is the relationship between mass and equilibrium displacement of the spring? There is a proportional relationship between the mass and the equilibrium displacement. When there was an increase in mass, the equilibrium displacement also increased. 2. Looking at Table 2, what can you conclude is the relationship between mass and the period of oscillation of the spring? The mass influences how large the period of oscillation will be. The larger the mass, the larger the oscillation. 3. In your oscillating mass simulation (Part 2 of the lab), try increasing “Spring strength” while maintaining mass. Is there any change in the period of the oscillation? Explain how this might be possible. The larger the spring strength value is, the harder it will be for the mass to pull on the string. This means the larger the spring strength, the smaller the period of oscilliations

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