Physics
Forced Oscillations
Quick fact
The Tacoma Narrows Bridge collapse in 1940 is a famous example of forced oscillations: wind provided a periodic force that matched the bridge's natural frequency, causing destructive resonance.
Why this is interesting
You've probably noticed that a swing can be pushed higher with small, well-timed pushes. But why does the same push feel useless at other times?
Read the full explanation
Understanding Forced Oscillations
Imagine a child on a swing. The swing has its own natural frequency—how often it rocks back and forth by itself after one push. Now, someone pushes the swing repeatedly. If the pushes happen at just the right time (matching the swing's natural rhythm), each push adds energy, and the swing goes higher and higher. That's a forced oscillation. If the pushes come at other times, they may cancel out or even slow the swing. The external force 'forces' the system to oscillate at its own frequency—the driving frequency. Even if the system originally oscillates at its natural frequency, the driven frequency eventually takes over (after a transient period), and the system settles into a steady-state oscillation at the driving frequency.
A deeper explanation
Every oscillating system has a natural frequency—the rate at which it vibrates when undisturbed. When an external periodic force is applied, the system is 'forced' to oscillate at the driving frequency. The amplitude of the resulting oscillation depends heavily on the difference between the driving frequency and the natural frequency. The closer they are, the more efficiently energy is transferred, and the larger the amplitude. When they are exactly equal, resonance occurs, producing maximum amplitude. In real systems, damping (energy loss from friction, air resistance, etc.) limits the amplitude; without damping, resonance would theoretically lead to infinite amplitude. Forced oscillations explain why a wine glass can shatter when a singer hits its natural frequency, why bridges must avoid matching wind frequencies, and how radio tuning works—each circuit's natural frequency matches a specific broadcast frequency. Understanding this concept helps engineers design safe structures and musicians control sound production.