Final answer:
The statement about the Tacoma Narrows Bridge is true; it collapsed due to resonance with wind-induced oscillations that exceeded its structural capacity, highlighting the importance of incorporating scientific principles in engineering design.
Step-by-step explanation:
The Tacoma Narrows Bridge collapse is a classic example of a structural design failure due to resonance. The bridge entered a harmonic oscillation when heavy cross winds matched its resonant frequency, with added complexity due to aeroelastic flutter. As the oscillations increased, the damping capacity decreased, especially after the support cables slipped over the towers. This led to amplitudes growing unchecked, resulting in the bridge's catastrophic failure.
Such cases underline the importance of applying mathematics and science to understand and predict how structures will react to environmental factors such as wind, and emphasize the need for adequate damping mechanisms to minimize the effects of resonance.