Forced Oscillation Resonance

Question

Maximum amplitude in forced oscillation occurs when driving frequency equals?

RankGuru · Accepted Answer

1. **Forced Vibration**: Occurs when a system is subjected to a periodic external driving force $F(t) = F_0 \cos(\omega_d t)$.
2. **Natural Frequency ($\omega_0$)**: The frequency at which the system oscillates if left alone after being disturbed.
3. **Resonance**: A phenomenon that occurs when the driving frequency matches the natural frequency ($\omega_d = \omega_0$).
4. **Outcome**: At resonance, the driving force is in perfect phase with the velocity of the system, allowing for maximum energy transfer and resulting in **maximum amplitude**.
5. **Note**: If damping is present, the peak amplitude occurs at a frequency slightly lower than $\omega_0$, but 'natural frequency' is the standard ideal answer.

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Forced Oscillation Resonance

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