5BL Lab 4 Manual - W24v3

Physics 5BL Lab 4 Manual: Oscillations Winter 2024, UCLA Department of Physics & Astronomy Directions: As you read through the lab manual, follow along and complete the Google Slides lab assignment submission template to submit your responses to prompts on each slide as indicated. Refer to your pre-lab for theoretical background, including key equations and definitions as needed. In this week’s lab, you will consider periodic , or oscillatory processes which have repetitive motion(s) in time. Specifically, you will compare and analyze the periodic motion of a simple pendulum and a mass on a spring. Experiment goals include understanding which physical factors affect the frequency of spring and pendulum oscillations. You will model the pendulum frequency depending on the length and the magnitude/direction of the gravitational acceleration of the pendulum. Your model for predicting the spring frequency depends on the mass on the spring and the spring constant k. Lab Procedure - Activity 1 We know that, in theory, the angular frequency of a mass on a spring can be found by using the equation ω = 𝑘 𝑚 where k is the spring constant and m is the mass. Your goal is to adjust these parameters and see how they affect the angular frequency of mass on a spring. 1. Using Hooke’s Law as a model for your spring, determine a method for measuring the spring constant. 2. Use the scale to verify the value of the hanging mass(es). 3. Using a stopwatch, measure the period of the oscillations of your first mass value. Consider: is it better to try to measure one period or a larger number of periods? 4. Convert your measured periods T to angular frequencies ⍵ = 2π/T. 5. Repeat the measurement with an increased value of the mass. 6. Now change the spring constant k, and repeat the measurements above with the same two mass values. To collect enough data, have each different lab member time the oscillations. You only need to report the average angular frequency. Lab Procedure - Activity 2 Your goals for this set of measurements include understanding which parameter(s) when changed affect the angular frequency of the simple pendulum. We know that, in theory, the angular frequency of a pendulum can be found by using the equation ω = 𝑔 𝐿 where g is the acceleration of gravity, and L is the length from the pivot point to the center of mass of the suspended object. Your goal is to adjust these parameters and see how they affect the angular frequency of the pendulum. 1. Measure the initial length L 1 carefully with the meter stick. 1

Physics 5BL Lab 4 Manual: Oscillations Winter 2024, UCLA Department of Physics & Astronomy 2. Using a stopwatch, determine the angular frequencies of oscillation for your first simple pendulum setup. 3. Repeat your measurements with three additional lengths L 2 , L 3 , & L 4 . Tips: - To collect enough data, have each different lab member time the oscillations. You only need to report the average angular frequency. - Try to keep the angle at which you pull the pendulum back relatively small (less than 15°). - As the angle at which you pull the pendulum gets bigger, the frequency may be changed. Your textbook has some perspective on why this may be. - Note: the small angle approximation says that for small angles sin(x) ≅ x (in radians). You can investigate what constitutes a “small angle” by plugging in different angles in yourself. Just be sure to use radians in the equation and then convert to degrees if you want to think about the angle you deflected your pendulum in units of degrees. Lab Assignment: Slide 1: Experimental Setup & Model Application (Activity 1) - Describe your experimental setup, including your procedure for measuring the experimental spring constants k . - Calculate your theoretical angular frequencies using your 4 experimental setups (2 masses & 2 k -values). Describe overall trends predicted by your model for obtaining ⍵ (i.e, how will your results change as you vary your parameters for the mass-spring system?). Slide 2: Data, Analysis, & Conclusions (Activity 1) - Show the results from your four trials, using the table format from your pre-lab - Compute your percentage errors from your theoretical predictions and measured frequency values for each of your 4 trials - Compare results to your prediction - Discuss possible sources of error (and which error(s) you think is/are most likely and why). Be specific. Table 1: Experimental Results for Mass-Spring System: Mass-Spring System Trials: (mass 1) (mass 2) (spring constant 1), Trial 1: frequency, % diff. Trial 2: frequency, % diff. (spring constant 2) Trial 3: frequency, % diff. Trial 4: frequency, % diff. 2