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

In summary, the given problem involves a driven, undamped oscillator with varying amplitudes at different driving frequencies. The formula A = (F0/m)/(w0^2-w^2) can be used to solve for the resonant frequency, which is represented by \omega_0. By setting up and solving the equations with the given information, the resonant frequency can be determined.
  • #1
Varnson
23
0
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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  • #2
The resonant frequency is [tex]\omega_0[/tex]. It looks like you have two formulas, and two unknowns: [tex]F_0 / m[/tex] and [tex]\omega_0[/tex]. Should be solveable.
 
  • #3
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!
 

1. What is a driven, damped oscillator?

A driven, damped oscillator is a physical system that exhibits periodic motion, influenced by a driving force and a resistance force. It is characterized by a natural frequency of oscillation and a damping coefficient.

2. What is the equation of motion for a driven, damped oscillator?

The equation of motion for a driven, damped oscillator is given by:
m * x'' + c * x' + k * x = F0 * cos(ωt)

where m is the mass of the oscillator, c is the damping coefficient, k is the spring constant, F0 is the amplitude of the driving force, and ω is the angular frequency of the driving force.

3. How does damping affect the behavior of a driven oscillator?

Damping reduces the amplitude of the oscillator's oscillations over time, causing it to eventually come to rest. The amount of damping also affects the oscillator's natural frequency, with higher damping resulting in a lower frequency and vice versa.

4. What is resonance in a driven, damped oscillator?

Resonance occurs in a driven, damped oscillator when the frequency of the driving force matches the oscillator's natural frequency. This results in a large amplitude of oscillation, and can be seen as a peak in the amplitude-frequency graph.

5. How do you calculate the damping coefficient in a driven oscillator experiment?

The damping coefficient can be calculated by measuring the amplitude and frequency of the oscillator at different damping levels and fitting the data to the equation:
c = m * ωd / Q
where m is the mass of the oscillator, ωd is the damped frequency, and Q is the quality factor of the oscillator.

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