Cambridge Motion Help!!! (1 Viewer)

[ludac]

The rise and fall in sea level due to tides can be modelled by a SHM. On a certain day channel is 10m deep at 9 AM when it is low tide, and 16M deep at 4PM when it is high tide. If a ship needs 12M of water to sail down a channel safely, at wat times between 9AM and 9PM can the ship pass through. answer is 11:45 am to 8:15 pm. i hate this topic

 

[mirakon]

1. You have to get equation of form x= c + acos(nt) where c=centre a=amplitude.
2. c=13 as it is middle of 10 and 16 and a=3 as tide fluctuates by 3 to either side of centre
2.Low tide to high tide is half a period. Calculate time for a period.
3. T=period. Use formula T= 2pi/n to calculate n
4. Get equation in step 1, as you now know all the values
5. Sub the value x=12 for x then solve to find in between what times the ship can come in.

 

[ludac]

I used x=c+acos(nt+e). And i still dont get the right answer

 

[mirakon]

c=13
a=3
n= pi/7
e=0

did you get these values for your equation?

 

[ludac]

Yes, when i solve the equation i get stuffed up answer. I am doin something stupid.

 

[mirakon]

It would help if you post all the steps you did. Post your solution and I'll try to find out where you're going wrong. Note once you find the solution for t when you sub x=12 into your equation, express t in terms of hours then sub those hours into the times noting t=0 is 9am.

 

[ludac]

Well here is what i was doing. a=3, 14 = 2pi/n n=pi/7, x = 3cos(pi/7 + e), when t=0 , x= -3, -3 = 3cose, cose=-1, e= pi, x= 3cos(pi/7t + pi) Is this right?

 

[mirakon]

The 'e' is unnecessary, there is no shift in phase therefore e=0. Your equation is correct except e=0 and

x=13-3cos(pi/7t)

You need to shift the centre. The tides fluctuate 3m above and below 13 not 0 so 13 has to be your new centre. Check at t=0 x=10 (given in the question). If you're confused as to how I got the equation go through the steps I outlined again. Don't be discouraged, this is probably the hardest type of SHM question you're likely to get.

Good luck!