Physics Home > Teaching Labs > Mechanics > Normal Modes

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Lab Activities

In this lab, students examine the motion of a system of two or more coupled oscillators driven by an external periodic driving force. The oscillators are connected in such a way that energy is transferred back and forth between them, leading to coupled oscillations. Although this motion can be quite complex, it is possible to describe the motion of the entire oscillatory system in terms of n normal coordinates , which are linear combinations of the original coordinates. Conversion to the normal coordinates results in n independent equations in which the normal coordinates are uncoupled and each varies harmonically with time. This means that each normal coordinate can be considered as a single independent oscillator, called the normal mode, or eigenmode, that resonates its characteristic frequency, usually called the eigenfrequency. If non-linearity is neglected, any arbitrary undriven motion of the system can be analyzed into its normal mode components. The students examine systems that have from two to five normal modes.

Course Level

Intermediate

Student Handouts

Equipment

Number of set-ups available: 1 Per lab station: 1 air track/cover 1 air hose/2 hose clamps 1 air supply 6 air carts 6 matched 5 cm springs/box 2 7.5 cm springs 2 5 cm springs 1 MacScope Faraday sail 1 MacScope magnet apparatus 1 MacScope to magnet apparatus BNC cable/bent copper tubing 1 Macintosh/MacScope software 1 MacScope User's Manual 1 variable speed stepper motor to drive air carts/post and power cable 1 string to attach stepper motor disk to springs 1 string guide mounted on air track 1 Phillips 666 frequency counter/power cable 1 HP 54600 oscilloscope/power cable 2 BNC cables 1 BNC T-connector 4 thin metal plates for air cart 1 large metal bar for mounting on air cart 1 stand for frequency counter 1 balance/standard mass set 1 stopwatch 1 spring constant apparatus consisting of:      1 C-clamp      1 large metal bar (~1 meter)      1 short bar (~10 inches)      1 hooked collar sized to fit short bar      1 meterstick mounted on a post      2 ring stand clamps

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