A “CONCEPTUAL DESCRIPTION”:
Resonance is not something that just happens all of a sudden, but there is a dynamic process that leads to it that usually happens very fast. Most of the times the oscillator and the driving force (more simply, the hit) are not in phase. In these cases resonance will occur, but only after a while (a very little while). At first the system will be out of phase and gradually it will settle down into a stabilized mode – this is “phase locking”. This is the aspect of the resonance phenomenon that this simulation was designed to highlight. The idea of the simulation is to focus on the phases of the oscillator and the hit so we would be able to watch the phases move with reference to one another.
The bar animation representation at the bottom has two bars moving on the screen. One (red) represents the phase of the ball, and the other (blue) represents the time. Every time the blue bar passes the blue rectangle, there is a beep indicating that a hit is given. As these two bars move, the difference between them varies as a result of the hit given and also of the difference in frequencies.
There are three additional representations: (1) the oscillating object – the oscillator is represented by a ball moving back and forth; (2) the energy bar – indicating the energy of the oscillator; (3) the phase wheel – an arrow, representing the phase of the oscillator circling around;
The system has two modes – a manual mode and an automatic mode.
In manual mode, students can manually control the timing of each impulse. This is mainly to help one get the feel for how the simulation works and how some of the representations function. The bar animation is absent in manual model.
In automatic mode, the hit is given periodically.
The Rationale Behind the Feature (Specific Design Principle):
This simulation was designed and developed as part of our own struggling to understand some key aspects of forced oscillation and resonance. Conventional representations and simulations of forced oscillation and resonance fail to highlight some of these aspects, such as phase hops and phase locking. By designing a model of forced oscillation that highlights the phase of the oscillation and the phase of the driving force, we hope to provide some new ways of looking at the concept of oscillation.
Context of Use:
Our research group is examining ways to engage students in science (mainly Physics) topics through a new curricular focus on “Patterns of change and control”. The curriculum is organized around patterns that constitute powerful abstractions that join a wide range of superficially distinct phenomena, such as oscillation, exponential growth, exponential equilibration and more. We intend that students will use this simulation as part as their exploration of the oscillation pattern.
The scope of implementation is still very limited. Also, learning with this simulation has not been studied yet, so we cannot provide formal evidence of any kind. Still, preliminary use by students and adults in informal situations has elicited rich discussions and led subjects to some deep insights into the phenomenon/problem.