   # Mechanical Oscillations  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 Click the picture to see a mpeg movie of newsreel footage of the bridge's collapse (0.683 MB)

 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

## 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 ( t + ) Angular Frequency = 2 / T = 2 f Velocity v = - xm sin ( t + ) Acceleration a = - 2 xm cos ( t + ) Kinetic Energy K = mv2 = m 2 A2 sin2 ( t + ) Potential Energy U = kx2 = k A2 cos2 ( t + ) Total Energy E = kA2
The Linear Oscillator
 Angular Frequency Period Pendulums
 Torsion Pendulum Simple Pendulum Physical Pendulum Damped Harmonic Motion
 Displacement x(t) = xm e -bt/2m cos ( ' t + ) Angular Frequency Mechanical Energy (for b small) Forced Oscillations and Resonance d = # 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  ครั้งที่

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