Finding driving frequency.

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In summary, the natural frequency of a harmonic oscillator driven at its natural frequency by an outside force can be determined by taking the square root of the spring constant divided by the mass. The damping constant is not necessary for this calculation.
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Homework Statement



A harmonic oscillator is driven at its natural frequency by an outside force. If the spring constant is 187.5 N/m and the oscillator's mass is 26.1 kg, what is the driving frequency? The damping constant is 15.2 kg/s.


Homework Equations



w=omega=driving frequency
m(d^2x/dt^2)= -kx -b(dx/dt) + Fcos(wt)

x=Acos(wt+psi)

A= F/(m((wd^2-wo^2)^2 + (b^2)(wd^2/m^2))^.5

The Attempt at a Solution


We are given three of the necessary factors for the first equation but not x so I'm not sure if I can use it. I considered using the formula for Amplitude so that A=v/w. I also know that w=(k/m)^.5. However don't have force.
I don't have a great understanding of driven oscillations, (my book has all of 2 paragraphs on it) so any information is helpful. thanks
 
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  • #2
Unless you have a follow up question you don't need to know the damping constant. The natural frequency is defined as sqrt(k/m). Easy as that.
 
  • #3
Omy god. Thanks so much, I guess i got wrapped up in using the formula to calculate something.
 

1. What is driving frequency and why is it important in science?

Driving frequency refers to the frequency at which an external force is applied to a system. In science, it is important because it determines the response of a system, such as the amplitude or phase of a wave. It is also used to understand and manipulate various physical phenomena, such as resonance and oscillation.

2. How do scientists measure driving frequency?

Scientists measure driving frequency by applying a known external force to a system and measuring its response. This can be done using various techniques, such as frequency sweeps or Fourier analysis. The resulting data can then be used to determine the driving frequency of the system.

3. Can driving frequency be changed or controlled?

Yes, driving frequency can be changed or controlled by adjusting the external force applied to the system. This can be done by changing the frequency of the force or by changing the amplitude or phase of the force. Scientists can also manipulate driving frequency by using resonance or other physical properties of the system.

4. How does driving frequency affect resonance?

Driving frequency and resonance are closely related. Driving a system at its natural frequency, or its resonant frequency, can amplify its response. However, driving a system at a different frequency can cause destructive interference and decrease its response. Thus, understanding driving frequency is crucial in studying and utilizing resonance.

5. How is driving frequency used in real-world applications?

Driving frequency has various real-world applications, such as in electronics, acoustics, and mechanics. For example, in electronics, driving frequency is used to determine the response of circuits and filters. In acoustics, it is used to understand the properties of sound waves and create music. In mechanics, it is used to study the behavior of structures and materials under external forces.

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