What is the phase difference between the driving force and the displacement in a damped forced oscillator at resonance?

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Q: What is the phase difference between the driving force and the displacement in a damped forced oscillator at resonance?

Solution: At resonance, the phase difference is 90°.

Steps: 6

Step 1: Understand what a damped forced oscillator is. It is a system that experiences a driving force and has some resistance (damping).
Step 2: Know what resonance means. Resonance occurs when the frequency of the driving force matches the natural frequency of the oscillator.
Step 3: Recognize that at resonance, the system oscillates with maximum amplitude.
Step 4: Learn about phase difference. Phase difference is the angle by which one wave leads or lags another wave.
Step 5: In a damped forced oscillator at resonance, the driving force reaches its peak before the displacement of the oscillator does.
Step 6: Conclude that the phase difference between the driving force and the displacement at resonance is 90°.