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# Find the natural frequency?

For the system u"+3u=4sin(ωt), find the natural frequency, the value of ω that produces resonance and a value of ω that produces beats.

natural frequency=sqrt(3)

How do I find the beats?

### Comments

The answer for beats is ?=1.9 but I don't know how to find that.

I would like to get back to this unanswered question. Beats  are the result of two oscillations with different frequencies. I can't come up with the final answer because it should be some more data in the problem. Number "4" refers to the acceleration exerted by an external force. It defines the amplitude of oscillations, but not the frequency. Do you have any other infomation in your problem?

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Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.
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The general solution of this equation is

u = A sin (ω0t) + B cos(ω0t) + p sin(ωt)

where psin(ωt)  is a particular solution of the inhomogeneous equation. You can make sure that

p = 4/(3 - ω2)

while 3 = ω02 - square of natural frequency.

The frequaency of beats is the difference between natural frequency and  the frequaency of external force (ω). Thus it is equal to

Δω = √3 - ω.