Difference between forcing frequency and natural frequency

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SUMMARY

The discussion centers on the behavior of a one-dimensional discrete lattice subjected to sinusoidal forcing at a frequency \( w_0 \). It concludes that the vibrations of lattice points away from the origin will not match the forcing frequency but will instead align more closely with their natural frequencies as the distance from the origin increases. Additionally, the impact of the forcing frequency being within the pass-band or stop-band, or at a standing wave frequency, significantly influences the response of the lattice.

PREREQUISITES
  • Understanding of one-dimensional discrete lattice dynamics
  • Knowledge of natural frequency and its significance in mechanical systems
  • Familiarity with concepts of pass-band and stop-band in wave mechanics
  • Basic principles of sinusoidal forcing functions
NEXT STEPS
  • Research the effects of damping on lattice vibrations
  • Explore the mathematical modeling of discrete systems using differential equations
  • Study the implications of resonance in forced vibrations
  • Investigate the relationship between frequency response and material properties
USEFUL FOR

Mechanical engineers, physicists, and students studying wave mechanics or vibration analysis will benefit from this discussion.

Freakminer64
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If you force a one-dimensional discrete lattice to vibrate at the mass at the origin sinusoidally with forcing frequency w0, what will the frequency of vibrations be for the lattice points, NOT at the origin ? Will it be the natural frequency ? Or will it be close to the forcing frequency near the origin, but as you move further away from the mass that you are forcing the masses will vibrate at their natural frequency ?

What difference would it make if the forcing freq. was in the pass-band or stop-band or at a standing wave frequency ?
Thanks in advance
 
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