Real Time Measurement for Spring-Mass System: The Graphical and Mathematical Representations - Nurul Hidayat; Erni Yulianti (Postgraduate, University of Mataram, 2021)
Mathematics is the language of physics. The best way to describe a physical phenomenon is by describing its mathematical representations. In addition, viewing the graphical diagram of the corresponding mathematical expression is crucial to deeply understand the physical events. Therefore, setting simple experiments in real time to (1) observe the phenomena, (2) view the related diagrams, and (3) extract the mathematical representations is required. In this study, the real time and simple experimental set-up (consisting of ultrasonic sensor HC-SR04 connected to an Arduino Uno board) was designed to perceive the motion of a spring-mass system. The spring force, which is equal to the object’s weight, and displacement or spring elongation data were recorded for the object (with varying mass) attached to the spring. A small external downward force was given to stimulate the simple harmonic motion of the vertical spring-mass system. The displacement as the function of time of the spring-mass motion was recorded. With those measurements, the sinusoidal patterns, representing the simple harmonic motion characteristics, were also observed. The spring constants were 6.35(2) N/m and 6.26(1) N/m for the displacements measured by sensor and ruler, respectively. The periods form the angular frequency of the displacement function and from the spring constant (acquired from sensor data fitting) showed consistent results with very high accuracy. This simple experimental set-up is believed to fulfill the technological-based learning demand.