Lab Report 8 Outline for PHYS 2108

1 Name: Date: 10/26/2023 Partners: PHYS 2108 Section: Lab Title: Simple Harmonic Motion Lab Report 8 Prelab (2 points) Purpose This lab is to have hands on with Hooke’s Law and simple harmonic motion. This lab is to understand Hooke’s Law, Harmonic motion, and the impact of resonance. Procedure (Please keep under ½ page) Attach the spring to the hook and attach the hanger pan to the spring. This is the initial position. You add 25 g to the hanger pan each time and record the position. The Jolly Balance has the hanger pan with a 25 g attached. Stretch the hanger pan and release it. Record the time it takes to complete 20 oscillations. During Lab (Findings) Analysis (9 points) Data table 1: Hooke's Law Initial position of Hanger, x0 = 0.325m Added Mass Equivalent Force, F (N) Final Position, x f (m) Displacement x = x f - x 0 25 g 0.245 0.372 0.0470 50 g 0.490 0.417 0.0920 75 g 0.735 0.464 0.139 100 g 0.980 0.507 0.182 125 g 1.23 0.557 0.232 150g 1.47 0.602 0.277 Displacement of unknown mass: 0.368m

2 Data table 2: Simple harmonic motion Mass of hanger pan, m 0 = 50g Added mass, m i total mass, m = m i + m 0 (kg) time for 20 cycles (s) Period, T (s) Period Squared.T^2 (s^2) 25 g 0.0750 14.73 0.746 0.5424 50 g 0.100 17.1 0.854 0.729 75 g 0.125 18.8 0.942 0.887 100 g 0.150 20.4 1.02 1.04 125 g 0.175 22.5 1.13 1.27 150 g 0.200 23.4 1.17 1.37 % Error = 10% Reflection (6 points) 1. Zero is not included in the range of uncertainty for the y-intercept. The y-intercept represents the spring at its elongated position when there is not mass attached, this value should be zero because the spring is not subjected to any external force. If the y-intercept is not zero, an error in measurement or calculations of elongation or the spring could’ve occurred. 2. It was better to measure the time for 20 periods then divide by 20 because it allowed for a more accurate value. It would be hard to get an accurate time on one period because it was fast. By measuring 20 we can average the time. 3. A linear fit should not be used for the plot of period vs mass because the relationship between period and mass is not linear. The period of oscillation for a spring in a simple harmonic motion is given by the formula: T = 2pi * sqrt(m/K). T is the period, m is the mass attached to spring, and k is the spring constant. The period is proportional to the square root of the mass which means the relationship is not linear. 4. The range of uncertainty for the y-intercept of the plot of period squared vs mass should include zero. The y-intercept represents the period squared where there is no mass attached. The value should be zero because of period of oscillation when there is no mass attached is zero. Based on the period of oscillation in simple harmonic motion formula, the period is directly proportional to the square root of the mass. Therefore, when the mass is zero, the period is zero, and the period squared is zero. 5. The lab used different amplitudes to determine its impact of oscillation. The first trial had a 5 cm amplitude with a period time of 0.669 seconds. The second trial had a 10 cm amplitude with a 0.674 second period time. The difference between the two amplitudes is 0.0074 second. This concludes that the amplitude does not have an impact on the oscillation because the force that causes the spring to bounce back becomes larger with

4 Include lab summary/what you learned (1 points) and sources of error (1 point) We gained a deeper understanding about resonance, Hooke’s Law, and simple harmonic motion. Using multiple values gained from the lab to calculate spring constant. We used many values collected to find connections between displacement, frequency, amplitude, and energy. A possible error is the weight is not exactly 100 g.