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

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

Solution: At resonance, the phase difference between the driving force and the displacement is 180 degrees.

Steps: 5

Step 1: Understand what a damped oscillator is. It is a system that oscillates but loses energy over time due to damping forces like friction.
Step 2: Know what resonance means. Resonance occurs when the frequency of the driving force matches the natural frequency of the oscillator, leading to maximum amplitude of oscillation.
Step 3: Recognize that in a damped oscillator, the driving force and the displacement (the position of the oscillator) can be out of sync, or 'out of phase'.
Step 4: At resonance, the driving force is at its maximum, and the displacement is also at its maximum but in the opposite direction due to damping effects.
Step 5: Conclude that the phase difference between the driving force and the displacement at resonance is 180 degrees, meaning they are completely out of sync.