Frequency of Undamped, Forced Oscillation with Negligible Damping

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SUMMARY

The discussion centers on calculating the frequency of a mass-spring system undergoing undamped, forced oscillation. A 0.133 kg mass attached to a 6.80 N/m spring is driven by an oscillating force with an amplitude of 1.34 N, resulting in a desired vibration amplitude of 0.445 m. The correct frequency, calculated in radians per second, is determined to be 8.63 rad/sec, not Hz, highlighting the importance of distinguishing between these units in oscillation problems.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Familiarity with the formula for amplitude in forced oscillation
  • Knowledge of angular frequency (ω) and its relationship to frequency (f)
  • Basic skills in algebra for solving equations
NEXT STEPS
  • Study the derivation of the amplitude formula A=(F/m)/(sqrt(((ω^2 - ω₀^2)^2) + (bω/m)^2))
  • Learn about the concept of natural frequency (ω₀ = sqrt(k/m)) in mechanical systems
  • Explore the differences between frequency in Hz and angular frequency in rad/sec
  • Investigate the effects of damping on forced oscillation systems
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Students in physics or engineering, particularly those studying mechanics and oscillatory systems, as well as educators looking for examples of forced oscillation calculations.

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[SOLVED] Undamped, Forced Oscillation

Homework Statement


Damping is negligible for a 0.133 kg mass hanging from a light 6.80 N/m spring. The system is driven by a force oscillating with an amplitude of 1.34 N. At what frequency will the force make the mass vibrate with an amplitude of 0.445 m? There are two possible solutions, enter one of them.

Homework Equations


A=(F/m)/(sqrt(((w^2 - Wo^2)^2) + (bw/m)^2))
wo= sqrt(k/m)

The Attempt at a Solution


i filled in the equation, solved for w and got 8.63 Hz, but its wrong. A point in the right direction would do wonders.Cheers
 
Last edited:
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Did you get 8.63 Hz or 8.63 rad/sec?
 
the answer was rad/sec. i solved for w but put it in as the frequency. all i needed was a little nudge in the right direction. Thanks for your help!
 
Last edited:

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