Physics · Oscillations · NEET
Natural frequency (call it w0) is the frequency at which a body oscillates on its own after one push, decided by its own properties like mass and spring constant (w0 = root(k/m)). Driving frequency (call it wd) is the frequency of the outside periodic force that keeps pushing it. In a forced oscillation the body finally moves at the driving frequency wd, not at its own w0.
When the driving frequency equals the natural frequency (wd = w0), the outside force always pushes in the same direction as the body's motion. So every push adds energy at the perfect moment. Energy keeps building up and the amplitude grows very large. This matched condition is called resonance.
Damping (friction, air drag) removes energy from the system. If damping is small, the resonance peak is very tall and sharp - amplitude gets huge. If damping is large, the peak is short and wide - amplitude stays limited. In an ideal system with zero damping, amplitude at resonance would grow to infinity.
No. At the start there is a short transient where the body's own frequency shows up, but that dies out due to damping. In the steady state the body oscillates only at the driving frequency wd of the applied force, whatever its natural frequency w0 is.
Free oscillation: one push, no outside force after that, body moves at natural frequency w0 and amplitude slowly dies. Forced oscillation: an outside periodic force keeps acting, body moves at driving frequency wd. Resonance: the special forced case where wd = w0 and amplitude becomes maximum.
If a periodic force (marching soldiers, wind, a singer's voice) matches the natural frequency of a bridge or a glass, resonance builds huge amplitude. The large vibrations can crack the glass or break the bridge. That is why soldiers break step while crossing a bridge.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Resonance occurs when the driving frequency equals the natural frequency of the system, that is wd = w0. At this condition the amplitude of the forced oscillation is maximum.
No, resonance can occur without damping. But damping controls how large the amplitude gets. Less damping gives a taller, sharper resonance peak; more damping gives a smaller, broader peak.
A steady forced oscillation is a sinusoidal motion at the driving frequency, so it looks like SHM in form. But it is driven by an external force, unlike a free SHM which needs only one initial push.
Pushing a child's swing at the natural frequency makes it go higher each time. Other examples are a wine glass shattering at a singer's matching note and a radio tuned so its circuit frequency matches the station frequency.
The body immediately follows the new driving frequency in the steady state. The amplitude, however, depends on how close the driving frequency is to the natural frequency - it is largest near resonance.
