Resource Lesson
Vibrating Systems - Simple Pendulums
Printer Friendly Version
When the applied frequency generated by an outside source matches the natural frequency of a vibrating system,
resonance
occurs. Resonance states are not limited to
interference conditions
. For example, pendulums have a natural period of
where
L
represents the pendulum's length and
g
represents the gravitational field strength, or the local acceleration due to gravity which is commonly taken as 9.8 m/sec
^{2}
.
Let's consider a pendulum having a length 1 meter. Its period would be equal to
approximately 2 seconds. Therefore it has a
natural frequency
of
approximately f = ½ = 0.5 hertz.
If you were pushing a small child on a swing that was 1 meter long, you could push him once during each swing, that is once each 2 seconds; or you could push every other swing, once each 4 seconds; or push every third swing, once each 6 seconds.
Expressing these time intervals in terms of frequency, you could push at the following frequencies:
f = 1/2 = 0.50 hertz
f = 1/4 = 0.25 hertz
f = 1/6 = 0.17 hertz
That is, you can "drive" the pendulum's motion by applying an
external forced vibration
that either matches the pendulum's natural frequency or equals a sub-multiple of its natural frequency. In any of these instances, you could witness the swing's resonance by noticing its amplitude increasing with each push.
What would be first three time intervals at which you could push a small child in a swing that has a length of 2.25 meters that would result in resonance?
Related Documents
Lab:
Labs -
Directions: Constructive and Destructive Interference
Labs -
Doppler Effect: Source Moving
Labs -
Frequency of Vibrating Strings
Labs -
Illuminance by a Light Source
Labs -
Inertial Mass
Labs -
Interference Shading
Labs -
Pipe Music
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Sample Solutions
Labs -
Ripple Tank Student Involvement Sheet
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Speed of a Wave Along a Spring
Labs -
Speed of Sound in Air
Labs -
Speed of Sound in Copper
Labs -
Video: Law of Reflection
Labs -
Video: Law of Reflection Sample Diagram
Resource Lesson:
RL -
Barrier Waves, Bow Waves, and Shock Waves
RL -
Beats: An Example of Interference
RL -
Interference of Waves
RL -
Interference: In-phase Sound Sources
RL -
Introduction to Sound
RL -
Law of Reflection
RL -
Physical Optics - Thin Film Interference
RL -
Resonance in Pipes
RL -
Resonance in Strings
RL -
Ripple Tank Video Guides
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Sound Level Intensity
RL -
Speed of Waves Along a String
RL -
The Doppler Effect
RL -
Vibration Graphs
RL -
Wave Fundamentals
RL -
Waveform vs Vibration Graphs
REV -
Orbitals
Review:
REV -
Chapter 26: Sound
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Sound
REV -
Waves and Sound
REV -
Waves and Sound
Worksheet:
APP -
Echo Chamber
APP -
The Dog-Eared Page
CP -
Light Properties
CP -
Reflection
CP -
Shock Waves
CP -
Sound
CP -
Waves and Vibrations
NT -
Apparent Depth
NT -
Atmospheric Refraction
NT -
Concert
NT -
Light vs Sound Waves
NT -
Shock Cone
NT -
Sound Waves
NT -
Standing Waves
WS -
Beats
WS -
Beats, Doppler, Resonance Pipes, and Sound Intensity
WS -
Counting Vibrations and Calculating Frequency/Period
WS -
Doppler - A Challenge Problem
WS -
Doppler Effect
WS -
Fixed and Free-end Reflections
WS -
Fundamental Wave Terms
WS -
Illuminance 1
WS -
Illuminance 2
WS -
Interference: In-phase Sound Sources
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
More Practice with Resonance in Pipes
WS -
More Practice with the Doppler Practice
WS -
Practice with Resonance in Pipes
WS -
Practice with the Doppler Effect
WS -
Practice: Speed of a Wave Along a String
WS -
Pulse Superposition: Interference
WS -
Ripple Tank Review
WS -
Sound Vocabulary
WS -
Speed of Sound
WS -
Speed of Sound (Honors)
WS -
Standing Wave Patterns #1
WS -
Standing Wave Patterns #2
WS -
Standing Wave Patterns #3
WS -
Standing Wave Patterns #4
WS -
Vibrating Systems - Period and Frequency
WS -
Wave Phenomena Reading Guide
WS -
Wave Pulses
WS -
Waveform and Vibration Graphs #1
WS -
Waveform and Vibration Graphs #2
TB -
25A: Introduction to Waves and Vibrations
TB -
25B: Vibrations and Waves
TB -
25C: Wave Speed
TB -
25D: Interference
TB -
25E: Doppler
TB -
25F: Doppler Effect (continued)
TB -
26B: Speed of Sound
TB -
26C: Resonance
TB -
26D: Beats
TB -
26E: Decibels
TB -
27A: Light Properties
TB -
Decibels and Sound Intensity #1
TB -
Decibels and Sound Intensity #2
TB -
Interference Re-examined
TB -
Refraction Phenomena Reading Questions
TB -
Sound: Mixed Practice
TB -
Waves and Vibrations
PhysicsLAB
Copyright © 1997-2017
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton