Oscillation of Spring System with Decreasing Load
For the final project for UCLA's PHYS 4AL course (Physics Laboratory for Scientists and Engineers: Mechanics), our group decided to investigate oscillations of a spring-mass system which loses mass over time. Due to the shelter-in-place restrictions at the time (March 2021), our experimental setup used household materials to perform this experiment.
Our setup involved tying an exercise band to the pull-up bar of an exercise stand, determining its Hooke's Law constant, and recording its oscillations when attaching a sand-filled popcorn bucket with a hole in the bottom to allow outflow of mass over time. Data acquisition was performed using two cameras, a timer, an Arduino ultrasonic sensor, and a measuring tape for reference.
My role in the project was to derive the theoretical model expected of such an oscillation and perform experimental trials. Also under my responsibility were accounting for experimental controls to improve the accuracy and execution of our setup. One consideration I worked on was determining whether the assumption that mass decreases linearly from the system is valid. From calculating the mass flow rate of the sand, treating it like a fluid, for different heights of sand in the bucket and different hole diameters, I was able to determine a range in which the mass flow rate could be treated as linear. To experimentally verify the validity of the assumption, I modified the setup to include a mass scale below the sand stream and a timer to collect data for mass versus time in order to determine the mass flow rate out of the system.
Other considerations which I was responsible for were to include an LED and audio cue to synchronize the time scales of the two recording devices (one for the mass scale and another for the mass-spring system), making black tape markings on the bucket for the Tracker software to have a point to trace when acquiring data from the recordings, and to include a length scale reference by placing a measuring tape with markings in the same plane as the oscillation within the frame of the recording.
Additionally, I contributed towards data analysis by creating fit functions for the data and finding the best parameters for each trial using Python. I also attempted to find experimental frequency versus time, velocity and acceleration versus time, complex sine-wave fit functions, and calculus curvature over time for the data, though this analysis was not explore further due to time restrictions.
As a result of our group's effort, we received praise from the instructional team and earned an A for our project.
Our setup involved tying an exercise band to the pull-up bar of an exercise stand, determining its Hooke's Law constant, and recording its oscillations when attaching a sand-filled popcorn bucket with a hole in the bottom to allow outflow of mass over time. Data acquisition was performed using two cameras, a timer, an Arduino ultrasonic sensor, and a measuring tape for reference.
My role in the project was to derive the theoretical model expected of such an oscillation and perform experimental trials. Also under my responsibility were accounting for experimental controls to improve the accuracy and execution of our setup. One consideration I worked on was determining whether the assumption that mass decreases linearly from the system is valid. From calculating the mass flow rate of the sand, treating it like a fluid, for different heights of sand in the bucket and different hole diameters, I was able to determine a range in which the mass flow rate could be treated as linear. To experimentally verify the validity of the assumption, I modified the setup to include a mass scale below the sand stream and a timer to collect data for mass versus time in order to determine the mass flow rate out of the system.
Other considerations which I was responsible for were to include an LED and audio cue to synchronize the time scales of the two recording devices (one for the mass scale and another for the mass-spring system), making black tape markings on the bucket for the Tracker software to have a point to trace when acquiring data from the recordings, and to include a length scale reference by placing a measuring tape with markings in the same plane as the oscillation within the frame of the recording.
Additionally, I contributed towards data analysis by creating fit functions for the data and finding the best parameters for each trial using Python. I also attempted to find experimental frequency versus time, velocity and acceleration versus time, complex sine-wave fit functions, and calculus curvature over time for the data, though this analysis was not explore further due to time restrictions.
As a result of our group's effort, we received praise from the instructional team and earned an A for our project.
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