Physics
Forced Vibration
Quick fact
The Tacoma Narrows Bridge collapse in 1940 is a famous example of forced vibration—wind-driven oscillations matched the bridge's natural frequency, leading to catastrophic resonance.
Why this is interesting
Why can a singer shatter a glass with just her voice, and what causes a suspension bridge to collapse in a gentle wind? The answer lies in a deceptively simple phenomenon: forced vibration.
Read the full explanation
Understanding Forced Vibration
Imagine pushing a child on a swing. If you push at random moments, the swing moves irregularly. But if you push every time the swing comes back to you—timing your pushes with its natural rhythm—the swing goes higher and higher. In forced vibration, an external force (like your pushes) drives the motion of an object (the swing). The force repeats at a certain frequency—called the driving frequency. The object itself has a preferred frequency at which it naturally oscillates—its natural frequency. When these two frequencies match, the amplitude (how far the object moves) grows dramatically. That matching is called resonance. In real systems, friction (damping) limits the growth, but without enough damping, the vibrations can become dangerously large.
A deeper explanation
At its core, forced vibration is described by a differential equation that includes the external driving force. The system's response depends strongly on the ratio of the driving frequency to the natural frequency. When the driving frequency is much lower than the natural frequency, the system moves in step with the force at low amplitude. When much higher, the system barely responds. But near the natural frequency, the amplitude peaks—this is the resonance peak. The width of that peak is determined by damping: light damping gives a sharp, high peak; heavy damping broadens and lowers it. This principle is used in tuning musical instruments (designing for resonance), but it also forces engineers to consider potential resonant failures in buildings, bridges, and machinery. Understanding forced vibration thus allows us to both exploit resonance for beneficial purposes and mitigate its destructive potential.