Mechanical math

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For a mechanical system with two degree offreedom, the motion of the two particles is different from the much easier simple harmonic motion described previously. In general, the motion of & two (or greater) degree offreedora system is not sinusoidal.

However, there are situations (depending on the inrtial positions andvelocities of the individual particles) where each part of the system does oscillate sinusoidally with the same frequency. The particles complete each cycle together with the same period. These particular solutions to the equation of motion are called normal modes.

Definition : A normsl mode is a type of motion of a system of particles in which the displacemenrs of the particles all vary sinusoidally (with SHM) at the s ame angular frequency.

The number of normal modes correspond to the number of degrees offreedom.

The angular frequency of the sinusoidal motion is called normal mode angular frequency.

The two particles in the system can move in the same direction and such motion is said to be in-phose. When the two particles move in the opposite direction, then the motion is said to be phase-opposed.

Exercise 1.2 in page 9 illushates some of the above definitions.

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