Periodic Motion Lab

by Professor Rich Born

Introduction

Periodic motion is motion that repeats itself in regular intervals. If the motion has characteristics that are sinusoidal, then the motion is said to be simple harmonic (SHM). In this lesson, periodic motion that is not simple harmonic is studied. Never-the-less, the motion shows many characteristics of SHM, as can be seen when studying the position, velocity, and acceleration graphs. This lab makes use of PocketLab Voyager that has hitched a ride on an "intelino smart train" and is running on the VelocityLab app. Intelino is designed for all ages, has an intuitive app, has built-in sensors to provide an interactive experience for the user, and is easily programmed with color snaps that allow the user to control intelino's actions.

The PocketLab Voyager/intelino Periodic Motion Lab Setup

Voyager is attached to a measuring wheel with a 3M damage-free strip in the orientation shown in Figure 1. The measuring wheel consists of a pair of 3D printed wheels with rubber band tires, an axle, and a hitch. STL files are included with this lesson for the wheels, axle, and hitch. The hitch is attached to the intelino engine with a 3M damage free strip. The front of the intelino engine faces to the right. The weight of the measuring wheel plus Voyager is less than that of a pair of intelino wagons.

Intelino will go back and forth between a pair of reverse color snap commands, providing the periodic motion. For best results, the pair of color snap commands should be placed between 50 and 60 cm apart, and the engine should be running at the intelino autopilot speed "fast".

VelocityLab requires input on the diameter of the wheel to which Voyager was attached. This value, after adding the rubber band tires to the 3D printed wheel, was 6.5 cm. The z-axis is specified as the "axis of rotation" in the VelocityLab app. Make sure to orient Voyager to the wheel as shown in Figure 1, with the orange side of Voyager facing the wheel.

Figure 1 - The Voyager/intelino periodic motion lab setup

Video

The short 9-second video below shows a typical run of the periodic motion lab with Voyager and the Intelino smart train engine. The video shows VelocityLab displaying real-time position, velocity, and acceleration data as the engine moves back and forth.

Data Analysis

Figure 2 shows combined graphs of position, velocity, and acceleration vs. time. These graphs were constructed in Excel from data captured by VelocityLab as the intelino engine moved back and forth on the track. There are a number of questions that are worth discussing with students including those that follow. Questions 5 and 6 are intended for high school physics students only, as these two questions involve more advanced ideas.

1. What is the period of this motion in seconds? (Note that the period is the time for one complete back and forth oscillation. Period can be computed by determining the time between adjacent peaks in either position, velocity, or acceleration.)

2. Whenever the engine is centered between the reverse color snap commands, i.e., when the position is zero, what can be said about the velocity and acceleration? (The magnitude of the velocity, i.e., the speed, is near a max., The acceleration is near zero.)

3. Where is the engine located when the magnitude of the acceleration is a maximum? (The engine is at the reverse color snap commands, where the engine quickly stops and reverses itself.)

4. What can be said about the velocity when the magnitude of the acceleration is at a maximum? (The velocity is zero.)

5. The acceleration graph shows a negative peak at about 14 seconds. Where is the engine located then, and why is the acceleration negative? (The engine is located at the reverse color snap command on the far right. As it encounters this color snap command it is slowing down in the positive direction. As it starts moving away from this color snap, it is speeding up in the negative direction. In both cases, the acceleration is therefore negative.)

6. Discuss the idea that the instantaneous slope of points on the position vs. time graph gives the velocity, and the instantaneous slope of points on the velocity graph gives acceleration.

Figure 2 - Position, velocity, and acceleration vs. time for the periodic motion lab