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A level physics further mechanics question (2)

For this question I got part ii) but part b looking at the marscheme there are some points that I don’t understand:
-how is it in phase at 0.2Hz?
-why is the amplitude larger at 0.2Hz compared to 10Hz ?
-at resonance at 1.5Hz why is the phase difference 90, if they're the same isn’t the phase 0 ?
-at 10Hz why is the driver out of phase of pie ?IMG_6960.jpeg
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(edited 2 months ago)
Hi! Sorry for the really late response, but this might still be helpful:

At resonance, the driving frequency is not the same as the frequency of the system and it will always be 90' (π/2) out of phase. Below resonance, the driving frequency will be completely in phase with the system, including at 0.2Hz. Above resonance, the frequency will be greater than π/2 out of phase, which is why destructive interference occurs and the amplitudes decreases as the driving frequency continues to increase. I believe this is true for all SHM questions.

in response to these questions:
-why is the amplitude larger at 0.2Hz compared to 10Hz ?
-at 10Hz why is the driver out of phase of pie ?

10Hz is very far from resonance compared to 0.2Hz, so it will have a much smaller amplitude. The amplitude will be very small and close to complete destructive interference (almost not oscillating at all), therefore the phase difference will be approx π.

^^might need a quick fact check on what I have said, but I think this is all correct (I compared it to a couple other websites)

Hope this helps in some way :smile:

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