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# OCR A2 Physics 2011 January Exam question 4 help please - Simple Harmonic Motion watch

I'm doing question 4 on the 2011 January past paper, I did all the first parts of the questions completly fine until I got to the last part, part (iii) where you have to give and expression for the depth of the water.

I got d = 2.5cos(1.39x^10-4 x t)

but in the mark scheme the answer is what I have but plus 15.5:

d = 15.5 + 2.5cos(1.39x10^-4 x t)

My question is why is it plus 15.5. Is it the Amplitude minus the max water level, but I don't understand why that needs to be added. Please let me know why the 15.5 is there. Thanks

2. (Original post by Reda2)

I'm doing question 4 on the 2011 January past paper, I did all the first parts of the questions completly fine until I got to the last part, part (iii) where you have to give and expression for the depth of the water.

I got d = 2.5cos(1.39x^10-4 x t)

but in the mark scheme the answer is what I have but plus 15.5:

d = 15.5 + 2.5cos(1.39x10^-4 x t)

My question is why is it plus 15.5. Is it the Amplitude minus the max water level, but I don't understand why that needs to be added. Please let me know why the 15.5 is there. Thanks

The depth of the water at time t would be the 'resting' water level plus the displacement due to the tide. The resting level would be the midpoint of 13 and 18, so 15.5. I can't think of a better way to describe resting level but if you just imagine there is no tide and the water isn't undergoing simple harmonic motion, or the water level when the displacement is 0.

Does that make sense?
3. (Original post by Alex621)
The depth of the water at time t would be the 'resting' water level plus the displacement due to the tide. The resting level would be the midpoint of 13 and 18, so 15.5. I can't think of a better way to describe resting level but if you just imagine there is no tide and the water isn't undergoing simple harmonic motion, or the water level when the displacement is 0.

Does that make sense?
Yes it does, thank you very much! I understand it now.

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