The motion of a motor-driven ball rotating in a circle is shadow-projected. It is shown to coincide with the motion of a mass on a spring executing simple harmonic motion at the same frequency.
Demonstration Instructions: Use light source and screen to shadow project motion of balls.
A spring undergoes simple harmonic motion (SHM) in the vertical direction. SHM occurs when the restoring force (in this case, the spring force) is proportional to the displacement. Another ball is made to rotate at a constant angular frequency in the vertical plane and its shadow undergoes SHM. This is because the projected acceleration of the rotating ball on the vertical axis is directly proportional to y (the ball's displacement). Consequently, the shadow exactly mimics the motion of the spring.
Row I (back wall)
See page 421, University Physics, for information regarding simple harmonic motion.
Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky's University Physics: With Modern Physics, 12th ed. San Francisco: Pearson Addison-Wesley, 2008.