sdfs_logosoundlogo

Mechanical Resonance

  • Introduction
  • Video & Results
  • Materials
  • Procedure
  • Preparation & Notes
  • Download Files

Introduction

In these activities students will:

  1. Relate the length of a pendulum to its period and frequency
  2. Observe mechanical resonance energy transfer (coupled harmonic oscillations) between two pendulums
  3. Observe that pendulums that do not swing with an appropriate period will not transfer energy between each other.

Background

Objects and structures have natural resonant frequencies of vibration or oscillation. When a pendulum swings, it has a natural frequency or period. The period of a pendulum is the time it takes to swing back and forth one time. Pipes have natural frequencies that resonance when tapped or when wind blows through them.

Bridges and buildings have natural vibrational frequencies. The colllapse of the Tacoma Narrows bridge in November 1940 is a famous example of mechanical resonance energy transfer. Winds of 35-46 mi/hours (65-75 km/hr) produced oscillations in the bridge (1) harmonic with the natural frequencies of the structure, leading to a dramatic increase in the amplitude of the vibrations, and ultimately the collapse.

Video of the Tacoma Narrows Bridge Collapse

(1) http://www.math.harvard.edu/archive/21b_fall_03/tacoma/index.html

Video

Coupled Harmonic Oscillation
Two pendulums of the same length will have the same frequency of oscillation, and will be able to transfer energy back and forth. Another terms for this phenomenon is Mechanical Resonance Energy Transfer.

In this video, one pendulum is swung. Watch for:

  1. Over time the pendulum of matching length begins to swing with the same frequency.
  2. The longer and shorter pendulums are relatively still.
  3. Eventually the matched pendulum swings with greater amplitude (swings wider) than the pendulum originally tipped (0:13 ).
  4. Later, the energy is transferred back to the first pendulum (0:20).

 

Inharmonicity: Uncoupled Oscillations

In this video the long pendulum swings while the other pendulums remain relatively motionless because the natural frequency of the oscillations of the others do not match the long pendulum. This pendulum swings at the lowest frequency of the four, (and has the longest period).

In this video, the shortest pendulum is swinging. It's motion back and forth demonstrates the highest frequency and shortest period of the for pendulums. Can you relate these facts to what you may have already learned about tuning forks, frequency and pitch?

Materials

Swinging Coupled Harmonic Oscillation

  • 2 pieces of wood. eye_bolt
    3 ft 1"x4"
    2 ft 1"x2"
  • 2 medium eye hooks for supporting the 1"x2"
  • 6 cup hooks, or similar (ACE Hardware part# 5329644)
  • 4 heavy eye bolts (6" x 1/2", shown right) for weighting pendulums
  • 4 pieces of string with loops on the ends,
    2 of matched length, (we used 5", 9", 9" and 18")
  • 2 chairs of tables for supporting the top board

Procedure

Swinging Coupled Harmonic Motion

  1. Hold the eye bolt attached to the shortest string (our short pendulum) and start it swinging. Observe its motion and the motion of the other pendulums. When you are done observing, hold all the pendulums still.

  2. Once all the pendulums are still, hold the longest pendulum and start it swinging. Observe its motion and the motion of the other pendulums.
    Are the other pendulums swinging?
    How fast does this pendulum swing back and forth relative to the short pendulum? Describe its motion using terms like frequency and period.


  3. Once all pendulums are still, hold one of the two medium length pendulums and swing. Observe the motion of the other pendulums. Pay close attention to the pendulum of the same length, you will notice some "coupling" of their motions.

The Resonator This activity comes from the exploratorium.

  1. Grip the Resonator on both ends and move back and forth length-wise on a table or floor. Which of the 4 balls moves the most (has the largest amplitude oscillation)?
  2. Now increase how fast the Resonator is moved back and forth and see if you can get a ball on a shorter dowel to move faster than the ball on the longest dowel.
  3. Experiment with different speeds. You might find that at some speeds of movement, that the some dowels hardly move and some move wildly.

When a dowel moves wildly, you have matched its natural resonant frequency with the frequency of the back and forth movement.

Preparationswing_setup

Mounting the pendulums

  1. Screw 2 eye bolts into the 2"x4" piece of wood as shown, about 10" apart in the center of the board.
  2. Line up the 1"x4" wood and screw in the cup hooks the so that the 1"x4" lines up centered on the 2"x4" and can hang from the eye bolts. These hooks will be on the top side of the 1"x4".hook bolt
  3. Attach the cup hooks to the bottom side of the 1"x4" space apart so that the pendulums can swing without touching each other.

Download files

References

The Resonator A great activity that demonstrates coupled motions. from the Exploratorium in San Francisco.l