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?
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?
The general solution of this equation is
u = A sin (ω_{0}t) + B cos(ω_{0}t) + p sin(ωt)
where psin(ωt) is a particular solution of the inhomogeneous equation. You can make sure that
p = 4/(3 - ω^{2})
while 3 = ω_{0}^{2} - 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.
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?