What Is the Driving Frequency of a Harmonic Oscillator with Given Parameters?

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The discussion focuses on calculating the driving frequency of a harmonic oscillator given a spring constant of 187.5 N/m and a mass of 26.1 kg. The natural frequency is determined using the formula w = sqrt(k/m), which simplifies the problem. The damping constant of 15.2 kg/s is mentioned but deemed unnecessary for this specific calculation. Participants emphasize the importance of understanding driven oscillations and clarify that the natural frequency is the key factor. The conversation concludes with a realization that the initial approach was overly complicated.
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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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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.
 
Omy god. Thanks so much, I guess i got wrapped up in using the formula to calculate something.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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