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# normal - Normal Modes Objective To investigate the behavior...

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Normal Modes Objective: To investigate the behavior of a mechanical system Apparatus: Vibrating Strip apparatus, small foam pads (2), small aluminum block (1), Read/Drive cable patch panel, PC sound card interface, speakers, FFTScope software, cables; Two pendulums coupled with spring, motion sensor, supporting beam, ring stand. Introduction One of the last labs you performed last semester in 229 was the RLC Circuits experiment. In that lab you examined how energy was shuttled back and forth between the Inductor (L) and Capacitor (C) of the circuit, resulting in an oscillation:

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Some important results you got from that lab were: 1. There is no oscillation if only C exists in a circuit, without L; you get only exponenential decay. Both L and C are needed to exchange enery constantly. 2 The amplitude of oscillation dies down due to energy being dissipated through the Resistor (R). R provides damping for the oscillator. 3. The circuit provided the maximum response amplitude when driven at the characteristic frequency ω 0 . This is the "natural" frequency at which an oscillator likes to oscillate. 4. The phase or difference in synchronization between the driving voltage and the response voltage is zero at the characteristic frequency ω 0 . This means that if you drive a system at its natural frequency, you will get the maximum response - think of you and a friend trying to dislodge a car stuck in the snow: you move the car by pushing it at precisely the same time it rocks away from you. (If you chose to push while it was coming toward you, you would just kill the rocking. Think of pushing a swing, as well. In this lab, your systems will be a mechanical, rather than electrical. It will also have various ways to oscillate (note that the circuit only had one way - for energy or charge to oscillate between L and C). The first system consists of a thin metal strip, which is fixed at both ends. It has more than one mode of vibration; its normal modes are listed below:
From top to bottom, the normal modes are: 1. Stationary (not moving) 2. Symmetric mode (both left and right sides of the strip move in the same direction at the same time). 3. Antisymmetric mode (left and right sides of the strip move in opposite directions at the same time). 4. Torsional mode (twisting along the length of the strip). There may be variations of this, and the above modes. Note that when this strip is made to vibrate by an external force at a specific frequency, it is said to be a Forced Harmonic Oscillator; otherwise it is is called a Harmonic Oscillator. Although the strip vibrates too quickly for your eyes to see, you can detect the frequencies of vibration of these modes using the FFT method you used last semester. Note that the strip has two magnets attached to its underside; they are there so that the

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normal - Normal Modes Objective To investigate the behavior...

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