What is the Resonant Frequency of a Driven, Undamped Oscillator?

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SUMMARY

The resonant frequency of a driven, undamped oscillator can be determined using the amplitude formula A = (F0/m)/(ω0² - ω²). In this discussion, the oscillator exhibits an amplitude of 3.0 cm at a driving frequency of 9 rad/s and 2.4 cm at 7 rad/s. By applying the provided formula and solving for the resonant frequency (ω0), users can derive the necessary value. The solution involves manipulating the equations to isolate ω0 as one of the unknowns.

PREREQUISITES
  • Understanding of driven, undamped oscillators
  • Familiarity with the amplitude formula A = (F0/m)/(ω0² - ω²)
  • Basic knowledge of angular frequency (ω)
  • Ability to solve algebraic equations with multiple variables
NEXT STEPS
  • Practice solving problems involving driven, undamped oscillators
  • Learn about the effects of damping on oscillators
  • Explore the concept of resonance in mechanical systems
  • Study the relationship between frequency, amplitude, and force in oscillatory motion
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Students in physics or engineering courses, particularly those studying oscillatory motion and resonance phenomena.

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Driven, damped oscillator - URGENT!

Homework Statement


A driven, undamped oscillator has an amplitude of 3.0cm at a driving frequency of 9 rad/s and an amplitude of 2.4cm at a driving frequency of 7 rad/s. What is the resonant frequency of the oscillator?


Homework Equations


A = (F0/m)/(w0^2-w^2)


The Attempt at a Solution


My prof. gave me the above formula as a hint, but I have no idea where to start from and what to do. Thanks for the help!
 
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The resonant frequency is \omega_0. It looks like you have two formulas, and two unknowns: F_0 / m and \omega_0. Should be solveable.
 
I solved it, for some reason I just couldn't see it adn it was sitting in front of me lol. Thanks for the help!
 

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