Forced Oscillations And Resonance

When an external periodic force drives an oscillator, the steady-state amplitude depends sharply on how the driving frequency compares to the system's natural frequency. Resonance is the condition where the driving frequency matches the natural frequency, allowing energy to be fed into the system most efficiently each cycle so the amplitude grows to a maximum. At resonance the driving force stays in step with the velocity of the oscillator, doing positive work throughout each cycle and continually pumping in energy. The option of a much higher driving frequency is wrong because the oscillator cannot keep pace, and the response amplitude actually falls off well above resonance. The option of half the natural frequency does not produce the primary resonance peak for a simple driven oscillator and transfers energy inefficiently. The option of a driving frequency approaching zero merely shifts the oscillator slowly with the force and gives only a small static-like displacement. This is the NCERT description of forced oscillations and resonance, where amplitude peaks as driving frequency nears natural frequency. As a plausibility check, everyday experience confirms that pushing a swing in step with its natural rhythm produces the biggest arc, exactly the resonance condition described here.