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

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The discussion centers on determining the resonant frequency of a driven, undamped oscillator given specific amplitudes at different driving frequencies. The amplitude is 3.0 cm at 9 rad/s and 2.4 cm at 7 rad/s, with the relevant formula provided as A = (F0/m)/(ω0² - w²). Participants note the challenge of solving for the resonant frequency (ω0) due to having two unknowns. Ultimately, one participant successfully solves the problem after initially struggling to see the solution. The conversation highlights the importance of understanding the relationship between amplitude and frequency in oscillatory systems.
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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!
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
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