GertieS.gif (35899 bytes)

Mechanical Oscillations

torsion.gif (38031 bytes)

tacoma_narrows1.gif (10376 bytes)
Click picture to see an mpeg movie of the collapsing bridge
(7.659 MB)
The Tacoma Narrows Bridge or "Galloping Gertie" as it was sometimes called, fell only four months after its completion because winds plowing to Puget Sound caused the bridge to resonant and collapse.  You can read the Washington Department of Transportation's A Short History Of Galloping Gertie.  You may also look at the traffic on the new Tacoma Narrows Bridge tacoma_narrows2.gif (7430 bytes)
Click the picture to see a mpeg movie of newsreel footage of the bridge's collapse (0.683 MB)

Visit The Harmonic Oscillator to learn more about the kinematic equations for a spring.


Previously Asked Questions

Q:     At the Hansen Planetarium in Salt Lake City, UT, USA there is a giant pendulum that keeps track of time by knocking over pegs placed around a circle.  What kind of pendulum is this and how does it work?

A:     This museum exhibit is called "The Foucault Pendulum" and can be seen in many museums around the world.  Characteristic for the Foucault Pendulum is the very, very long cord (or wire, or beam) that supports it to a fixed point above the mass of the pendulum.   When the oscillating pendulum knocks over successive pairs of diametrically opposite pegs, what moves is in fact not the vertical plane in which the pendulum oscillates but the surface of the earth with which the pegs are connected.  After each twenty-four hour time period, one full rotation of the earth is completed and the Foucault Pendulum will knock over the same pair of pegs.

Visit the Hansen Planetarium

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References

Equations

Frequency 1 hertz = 1 Hz = 1 oscillation per second =   1 s-1
Period T = 1 / f
Simple Harmonic Motion
Displacement x = xm cos (omega2.gif (834 bytes)t + phi2.gif (845 bytes)
Angular Frequency omega2.gif (834 bytes) = 2pi2.gif (831 bytes) / T = 2pi2.gif (831 bytes) f
Velocity v = - omega2.gif (834 bytes) xm sin (omega2.gif (834 bytes)t + phi2.gif (845 bytes)
Acceleration a = - omega2.gif (834 bytes)2 xm cos (omega2.gif (834 bytes)t + phi2.gif (845 bytes)
Kinetic Energy K = onehalf.gif (67 bytes) mv2 = onehalf.gif (67 bytes)m omega2.gif (834 bytes)2 A2 sin2 (omega2.gif (834 bytes) t + phi2.gif (845 bytes)
Potential Energy U = onehalf.gif (67 bytes) kx2 = onehalf.gif (67 bytes) k A2 cos2 (omega2.gif (834 bytes) t + phi2.gif (845 bytes)
Total Energy E = onehalf.gif (67 bytes) kA2
The Linear Oscillator
Angular Frequency

16-11.gif (216 bytes)

Period

16-12.gif (251 bytes)

Pendulums
Torsion Pendulum 16-25.gif (172 bytes)
Simple Pendulum 16-29.gif (178 bytes)
Physical Pendulum 16-32.gif (202 bytes)
Damped Harmonic Motion
Displacement x(t) = xm e -bt/2m cos (omega2.gif (834 bytes)' t + phi2.gif (845 bytes)
Angular Frequency 16-41.gif (335 bytes)
Mechanical Energy (for b small) 16-42.gif (251 bytes)
Forced Oscillations and Resonance omega2.gif (834 bytes)d = omega2.gif (834 bytes)

[Top] [Previously Asked Questions] [References]


Mechanics List of Topics

Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of
Rigid Bodies
Elasticity
Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical
Oscillations
Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves
Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy
and Work
Circular Motion of Point-Mass Objects Equilibrium Sound

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