Mechanical resonance Mechanical resonance Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its "resonance frequency" or "resonant frequency") than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings and airplanes. This is a phenomenon known as resonance disaster. Avoiding resonance disasters is a major concern in every building, tower and bridge construction project. The Taipei 101 building relies on a 660-ton pendulum—a tuned mass damper—to modify the response at resonance.
Negative frequency is just a constant whose amplitude level is a measure of the strength of the original "ω" content. And whatever part of "x"("t") that was at frequency zero is changed to a sinusoid at frequency −"ω". Similarly, all other frequencies are changed to non-zero values. As the interval increases, the contribution of the constant term grows in proportion. But the contributions of the sinusoidal terms only oscillate around zero. So "X"("ω") improves as a relative measure of the amount of frequency "ω" in the function "x"("t"). The Fourier transform of formula_1 produces a non-zero response only at frequency "ω". The