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Simple Harmonic Motion Demonstration Machine

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Submitted by Rich on Thu, 05/09/2019 - 14:52

Introduction

In a well-known 1938 book entitled "Demonstration Experiments in Physics", editor Richard Sutton describes a device that produces simple harmonic motion (SHM) mechanically.  With today's tremendous growth in the 3D printing industry, such a device can now be easily constructed for classroom demonstrations of SHM.  Couple this device with PocketLab Voyager and you can obtain real-time graphs describing the motion.

Description of the Simple Harmonic Motion Machine

Figure 1 shows the 3D printed SHM machine constructed by the author of this lesson.  All required 3D printer files are included with this lesson.

The 3D Printed Simple Harmonic Motion Machine
Figure 1 - 3D printed simple harmonic motion machine

The handle on the back of the SHM machine is used to turn a circular wheel with a pin near the edge of the front of the wheel.  The pin protrudes through a vertical bar having a slot.  The length of the slot is slightly larger than the diameter of the wheel.  The width of the slot is just a little larger than the diameter of the pin.  While the wheel is turned uniformly by a student, the pin executes a circle.  The slotted vertical bar has horizontal bars attached to its center that are free to move back and forth in two supports at the front of the SHM machine.  PocketLab Voyager is attached to the top of the slotted vertical bar with its range finder facing a piece of white cardboard.  The range finder then captures the position of the vertical bar as a function of time.  In summary, the slotted vertical bar describes only the horizontal component of the pin's motion.  If the wheel is rotated uniformly, then the resultant motion will be simple harmonic. 

The wheel support and the two horizontal bar supports are attached to a board with strong double-sided tape.

Simple Harmonic Motion Machine Video

The 17-second video below shows the simple harmonic motion machine in action.  PocketLab Voyager's range finder data is displayed in real-time on a Chromebook running the PocketLab app.

Constructing the Simple Harmonic Motion Machine

There are five 3D printer .stl files accompanying this lesson.  Included in the SHMHardware.stl file are an indicator mount screw and nut licensed under Creative Commons by idkmsu.   https://www.thingiverse.com/thing:2422279

Probably the best way to learn how to construct the SHM machine is via some photos.  Figure 2 shows the front view and Figure 3 shows the rear view of the SHM machine.

SHM machine front view
Figure 2 - SHM machine front view
SHM machine rear view
Figure 3 - SHM machine rear view

Figure 4 shows the details of the hardware construction on the axle wheel platform.

SHM axle closeup
Figure  4 - SHM machine axle closeup

Additional PocketLab Lessons on Simple Harmonic Motion

There are numerous lessons on the PocketLab web site related to simple harmonic motion.  Click here for a list of these lessons.

3D Printed Simple Harmonic Motion Machine