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

[rockettanakit]

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((w_d^2-w_o^2)^2 + (b^2)(w_d^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

 

[Mindscrape]

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.

 

[rockettanakit]

Omy god. Thanks so much, I guess i got wrapped up in using the formula to calculate something.