What happens when ...
... the forcing frequency (w2) equals the natural frequency (w1) in a solution for an undamped system?
When w1 = w2, we encounter such events like the Tacoma Narrows Bridge disaster.
The function can also describe sound. Feedback occurs when w1 = w2. When w1 does not equal w2, we can obtain a harmonic resolution. Ain't that just beautiful! More on the Theory of a Musical Universe.
Consider the ODE mx'' + kx = Fcos(w1t)
And the soln .. x(t) = Acos(w1t) + Bsin(w2t) + ((F/m)/(w1^2 - w2^2)).
And the soln .. x(t) = Acos(w1t) + Bsin(w2t) + ((F/m)/(w1^2 - w2^2)).
When w1 = w2, we encounter such events like the Tacoma Narrows Bridge disaster.
The function can also describe sound. Feedback occurs when w1 = w2. When w1 does not equal w2, we can obtain a harmonic resolution. Ain't that just beautiful! More on the Theory of a Musical Universe.
posted by dc @ 6:00 PM
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