Physics · Oscillations · NEET
A free oscillation is the to-and-fro motion of a body after you give it just one push or one pull and then leave it. No outside force acts on it after that first disturbance. A simple pendulum pulled to one side and released, or a spring-mass stretched once and let go, both do free oscillations. The only forces acting are the internal restoring force and (in the ideal case) nothing else.
Natural frequency is the frequency at which a body oscillates freely, on its own. It is fixed by the body's own properties. For a spring-mass system, natural frequency f = (1/2 pi) times root(k/m), so it depends on spring constant k and mass m. For a simple pendulum, f = (1/2 pi) times root(g/L), so it depends on length L and gravity g. It does NOT depend on how far you pulled it (the amplitude).
No. This is the most common confusion. In free oscillation (SHM), the natural frequency stays the same whether the amplitude is small or large. A bigger pull gives more energy and a bigger swing, but each swing still takes the same time. This is called isochronism. Only mass, stiffness, length or g can change the natural frequency.
An ideal free oscillation with small displacement is SHM, because the restoring force is proportional to displacement (F = -kx). But the words describe different things. SHM describes the shape of the motion (sine wave, F proportional to -x). Free oscillation describes the cause: one push, then no external force. In NEET, an ideal free oscillation is treated as SHM with constant amplitude.
In real life, friction and air resistance take energy away on every swing. So the amplitude keeps getting smaller until the body stops. This is called damping, and such motion is damped oscillation. A perfectly free oscillation (no friction) would keep the same amplitude forever, but that is an ideal case. The natural frequency in light damping is almost the same as the ideal natural frequency.
Free oscillation: pushed once, then no outside force, swings at natural frequency, constant amplitude in the ideal case. Damped oscillation: pushed once, but friction slowly reduces the amplitude to zero. Forced oscillation: an outside periodic force keeps pushing it, so it finally swings at the driving force's frequency, not its own natural frequency. When the driving frequency equals the natural frequency, you get resonance (very large amplitude).
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A free oscillation is when a body swings on its own after a single push. Example: a child's swing pushed once and then left alone, or a guitar string plucked once. It vibrates at its natural frequency until friction stops it.
Natural frequency is the frequency at which a body oscillates freely by itself, decided only by its own mass, stiffness, length or g, and not by the amplitude.
In light damping they are almost equal. Resonance happens in forced oscillation when the driving frequency matches the body's natural frequency, giving maximum amplitude. So the natural frequency is the frequency at which resonance occurs.
Spring-mass: f = (1/2 pi) times root(k/m). Simple pendulum: f = (1/2 pi) times root(g/L). Time period T = 1/f. These are the two most tested free-oscillation formulas.
For small displacement the restoring force follows F = -kx, which is the exact condition for SHM. So an ideal free oscillation with small amplitude is simple harmonic and has a constant natural frequency.
