In forced oscillation of a particle the amplitude is maximum...

In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force while the energy is maximum for a frequency $\omega_{2}$ of the force; then (A) $\omega_{1}<\omega_{2}$ when damping is small and $\omega_{1}>\omega_{2}$ when damping is large (B) $\omega_{1}>\omega_{2}$ (C) $\omega_{1}=\omega_{2}$ (D) $\omega_{1}<\omega_{2}$

In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force while the energy is maximum for a frequency $\omega_{2}$ of the force; then
(A) $\omega_{1}<\omega_{2}$ when damping is small and $\omega_{1}>\omega_{2}$ when damping is large
(B) $\omega_{1}>\omega_{2}$
(C) $\omega_{1}=\omega_{2}$
(D) $\omega_{1}<\omega_{2}$

Key Concepts

Energy Absorption in Oscillatory Systems

The energy absorbed by an oscillatory system in forced oscillation is influenced by both the amplitude of the response and the phase difference between the force and motion. In damped oscillators, maximum energy absorption can occur at a different frequency than maximum amplitude because the rate of energy input and the losses due to damping interact in a frequency-dependent manner.

Forced Oscillations

Forced oscillations refer to the response of an oscillatory system when an external periodic force is applied. In such systems, the motion is driven by this applied force, and the behavior of the oscillator, such as its amplitude and phase, depends critically on the frequency of the forcing relative to the system's natural properties.

Resonance

Resonance is the phenomenon where an oscillatory system experiences a significant increase in amplitude when the frequency of the external force approaches a particular value. This value is often near the system’s natural frequency, and the system responds most strongly as energy is most efficiently transferred from the driving force to the oscillator.

Damping

Damping introduces a loss mechanism in oscillatory systems, typically through frictional or resistive forces, which reduces the amplitude of oscillations over time. The presence of damping not only limits the maximum amplitude but also shifts the effective resonance frequency, affecting the overall response of the system to the applied force.

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