Damped Oscillations-A Smartphone Approach

Lat. Am. J. Phys. Educ. Vol. 3, No. 2, May 2009

We propose a new tool for laboratory curricula based on computer-aided data acquisition and analysis. A pendulum coupled to a low-friction rotary sensor offers variable length, variable mass, variable oscillation plane (to change the effective gravitational restoring torque) and two different kind of damping torque: “dynamic friction” (almost constant) and “viscous” proportional to the angular velocity. Simple models implemented in common spreadsheets allow to compare the experimental results with the theoretical predictions

arXiv (Cornell University), 2022

The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but colorful device that features longitudinal and torsional oscillations, catching the eye of students and teachers, and offering a fantastic environment to study coupled oscillations at qualitative and quantitative levels. However, the experimental setups that are commonly used to simultaneously acquire both oscillation types can be cumbersome and/or costly, often requiring two synchronised cameras, or motion sensors and photo-gates integrated by an expensive analog-to-digital converter. Here, we show that a smartphone can be the perfect device for recording the oscillations of a Wilberforce pendulum composed of just an educational helical spring and a can. Our setup employs a smartphone's accelerator and gyroscope to acquire data from the longitudinal and torsional oscillations, respectively. This setup can successfully record both normal modes and beats. Furthermore, we show that our experimentally obtained time-series and power spectra are in great agreement with simulations of the motion equations. In addition, we critically analyse how to set the initial conditions to observe both normal modes and beats. We believe our study contributes to bring the striking physics of the Wilberforce pendulum closer to undergraduate classrooms with low-cost, highly-accessible materials.

This paper looks at the physics behind oscillatory motion and how this can be applied to many different scenarios including using different types of pendulums to explain the phenomena of SHM and DHM (simple and damped harmonic motion respectively). Written as part of my A-Level Physics course (OCR B Advancing Physics) in Autumn 2014 (Nov 2014-Jan 2015)

arXiv (Cornell University), 2023

This paper aims to show how to guide students with a familiar example to extract as much physics as possible before jumping into mathematical calculation. The period for a physical pendulum made up of a uniform rod is changed by attaching a piece of putty on it. The period for the combined system depends on the location of the putty. Simple reasoning without calculation shows that there are two locations for the putty that do not change the period of the physical pendulum: the axis and the center of percussion. Moreover, without calculation, we reason that there is at least one minimal period when the putty lies somewhere between these two locations. The underlying physics is that the period depends on the ratio between two quantities: the torque and the momentum of inertia, which depends on the location of the putty. They conflict with each other; a smaller (larger) moment of inertia is accompanied by a smaller (larger) torque. The uniqueness of the minimal period and the corresponding location for the putty can only be obtained by calculation. Zee who also emphasizes thinking by quoting John Wheeler in the preface to his book [1]: Never never calculate unless you already know the answer! Another input is the qualitative analysis of simple harmonic motion, where the sinusoidal shape of the velocity versus time curve is not obtained by calculation but based purely on physical reasoning instead . The content of this article was tested in my Year-10 class. They enjoyed this style of teaching, so did I. The journey starts from the following two basic facts. The period for a simple pendulum with length ℓ and the period for a physical pendulum made up of a uniform rod with length 𝐿 are

Physics Education, 2010

The topic of coupled oscillations is rich in physical content which is both interesting and complex. The study of the time evolution of coupled oscillator systems involves a mathematical formalization beyond the level of the upper secondary school student's competence. Here, we present an original approach, suitable even for secondary students, to investigate a coupled pendulum system through a series of carefully designed hands-on and minds-on modelling activities. We give a detailed description of these activities and of the strategy developed to promote both the understanding of this complex system and a sound epistemological framework. Students are actively engaged (1) in system exploration; (2) in simple model building and its implementation with an Excel spreadsheet; and (3) in comparing the measurements of the system behaviour with predictions from the model.

The Wilberforce pendulum: a complete analysis using micro accelerometer/gyroscope, smartphone and dynamical modeling

The Wilberforce pendulum is a didactical device often used in class demonstrations to show the amazing phenomenon of coupled oscillations (rotational and longitudinal) producing beats in a special mass-spring set up. The phenomenon is particularly surprising for a distant observer, who easily detects the longitudinal motion, but may skip the presence of rotation. To him (her) the vertical oscillation appears to damp out completely and then it rises again without external action (as if an invisible force would come in). In this paper we propose a revised version of the classical experiment, suggesting a deeper understanding of phenomena through real time data acquisition of both the rotation and the vertical oscillation, using a MEMS accelerometer/gyroscope and the free software Phyphox to show the device motion on a smartphone screen. A detailed analysis of the motion and of the energetical aspects are then performed using the free modeling tool InsightMaker.

Presence of uncertainties or errors makes it possible to draw inference from the results obtained in experiments. Computerization of experiments increases the accuracy and precision of the results. In this paper, we are encapsulating these crucial aspects for studying the oscillations of a simple pendulum in order to determine the time period of the oscillations. The methods used are that of video analysis through Tracker software and model based simulations of Scilab software which are available on open source physics. Tracker reduces the errors involved in performing the experiment as compared to that performed manually. This is because of the temporal and spatial resolution associated with Tracker which leads to high precision and accuracy in the results obtained while analysing the captured videos of the simple pendulum oscillations. On the other hand, model based simulations is an effective tool to deal with the complexity involved in solving the equations associated with the s...

arXiv: Classical Physics, 2019

The characteristics of drive-free oscillations of a damped simple pendulum under sinusoidal potential force field differ from those of the damped harmonic oscillations. The frequency of oscillation of a large amplitude simple pendulum decreases with increasing amplitude. Many prototype mechanical simple pendulum have been fabricated with precision and studied earlier in view of introducing them in undergraduate physics laboratories. However, fabrication and maintenance of such mechanical pendulum require special skill. In this work, we set up an analog electronic simulation experiment to serve the purpose of studying the force-free oscillations of a damped simple pendulum. We present the details of the setup and some typical results of our experiment. The experiment is simple enough to implement in undergraduate physics laboratories.

2021

The development of a cost-effective experiment set is essential for teaching and learning physics in educational institutes. We aim to develop a computer-based simple pendulum experiment set consisting of a simple pendulum, infrared phototransistor, and Arduino board for calculating the gravitational acceleration (g). We used 13 pendulum lengths with five angles for each length to measure the period of motion. We found linear relationships between lengths and period-squared. The g-value was 9.806 ± 0.025 (average ± standard error) m/s2. Since this experiment set is costeffective, and more straightforward method to understand, it will benefit the physics learning in educational institutions.

2006

Experiments on the oscillatory motion of a suspended bar magnet throws light on the damping effects acting on the pendulum. The viscous drag offered by air was found the be the main contributor for slowing the pendulum down. The nature and magnitude of the damping effects were shown to be strongly dependent on the amplitude.