- Forums
###### M3 Further Dynamics - Simple Harmonic Motion HELP!

watch this thread

9 years ago

In a harbour, sea level at low tide is 10m below the level of the sea at high tide. At low tide, the depth of the water in the harbour is 8m. On a particular day, low tide occurs at 1pm and the next high tide occurs at 1:30am. A ship can remain in the harbour safely when the depth of water is at least 12m. The sea level is modelled as rising and falling with simple harmonic motion.

Find the length of time, on this particular day for which it is safe for the ship to remain in the harbour.

I have found the amplitude = 5. and w=2pi/25

However, in the solutions, it uses total time as 12.5 + 2t.

I understand the 12.5 hours is how long high tide lasts for as it will be over 18m for this length of time, but how does the 2t come about?

I would have thought total time would be (12.5 + t) when the tide is 12m and above.

Also, using x=asin(wt), the value of x is taken as 1, am I correct in assuming that x was calculated as being 13-12, where 13 is the middle of the amplitude with 8 being lowest and 18 being highest?

Many Thanks in advance!

Find the length of time, on this particular day for which it is safe for the ship to remain in the harbour.

I have found the amplitude = 5. and w=2pi/25

However, in the solutions, it uses total time as 12.5 + 2t.

I understand the 12.5 hours is how long high tide lasts for as it will be over 18m for this length of time, but how does the 2t come about?

I would have thought total time would be (12.5 + t) when the tide is 12m and above.

Also, using x=asin(wt), the value of x is taken as 1, am I correct in assuming that x was calculated as being 13-12, where 13 is the middle of the amplitude with 8 being lowest and 18 being highest?

Many Thanks in advance!

Reply 1

9 years ago

Original post by Coral Reafs

In a harbour, sea level at low tide is 10m below the level of the sea at high tide. At low tide, the depth of the water in the harbour is 8m. On a particular day, low tide occurs at 1pm and the next high tide occurs at 1:30am. A ship can remain in the harbour safely when the depth of water is at least 12m. The sea level is modelled as rising and falling with simple harmonic motion.

Find the length of time, on this particular day for which it is safe for the ship to remain in the harbour.

I have found the amplitude = 5. and w=2pi/25

However, in the solutions, it uses total time as 12.5 + 2t.

I understand the 12.5 hours is how long high tide lasts for as it will be over 18m for this length of time, but how does the 2t come about?

I would have thought total time would be (12.5 + t) when the tide is 12m and above.

Also, using x=asin(wt), the value of x is taken as 1, am I correct in assuming that x was calculated as being 13-12, where 13 is the middle of the amplitude with 8 being lowest and 18 being highest?

Many Thanks in advance!

Find the length of time, on this particular day for which it is safe for the ship to remain in the harbour.

I have found the amplitude = 5. and w=2pi/25

However, in the solutions, it uses total time as 12.5 + 2t.

I understand the 12.5 hours is how long high tide lasts for as it will be over 18m for this length of time, but how does the 2t come about?

I would have thought total time would be (12.5 + t) when the tide is 12m and above.

Also, using x=asin(wt), the value of x is taken as 1, am I correct in assuming that x was calculated as being 13-12, where 13 is the middle of the amplitude with 8 being lowest and 18 being highest?

Many Thanks in advance!

What time does t represent?

Reply 2

9 years ago

Original post by brianeverit

What time does t represent?

t represents the time that the water level will be 12m and above

Reply 3

9 years ago

Original post by Coral Reafs

t represents the time that the water level will be 12m and above

Do you mean the time from when it is 12 m to the time when it is a maximum?

If so, that would account for the multiplication by 2.

Reply 4

9 years ago

Original post by brianeverit

Do you mean the time from when it is 12 m to the time when it is a maximum?

If so, that would account for the multiplication by 2.

If so, that would account for the multiplication by 2.

Oh ok, so every 12.5 hours, water level fluctuates between 8m and 18m, so at high tide, am I correct in assuming, due to simple harmonic motion, that water is above 12m for 6.25h + t (as 13m is middle of amplitude, and the time for 12m-13m is t), and at low tide, from 8-13m, when it rises again from 8m to 13m it will be 6.25h + t?

so overall its 2(6.25h + t) = 12.5h + 2t?

does that sound correct? Is my thinking of simple harmonic motion accurate when I assume that for exactly half the time (12.5h) the water level rises and falls at a constant rate from 13m-18m, and 8m-13m?

Reply 5

9 years ago

Original post by Coral Reafs

Oh ok, so every 12.5 hours, water level fluctuates between 8m and 18m, so at high tide, am I correct in assuming, due to simple harmonic motion, that water is above 12m for 6.25h + t (as 13m is middle of amplitude, and the time for 12m-13m is t), and at low tide, from 8-13m, when it rises again from 8m to 13m it will be 6.25h + t?

so overall its 2(6.25h + t) = 12.5h + 2t?

does that sound correct? Is my thinking of simple harmonic motion accurate when I assume that for exactly half the time (12.5h) the water level rises and falls at a constant rate from 13m-18m, and 8m-13m?

so overall its 2(6.25h + t) = 12.5h + 2t?

does that sound correct? Is my thinking of simple harmonic motion accurate when I assume that for exactly half the time (12.5h) the water level rises and falls at a constant rate from 13m-18m, and 8m-13m?

If t is the ntime from a height of 12m to 13m then yes, that is correct.

Incidentally though, the water level NEVER rises or falls at a constant rate, but it will take the same time to rise and fall.

Reply 6

9 years ago

Original post by Coral Reafs

Oh ok, so every 12.5 hours, water level fluctuates between 8m and 18m, so at high tide, am I correct in assuming, due to simple harmonic motion, that water is above 12m for 6.25h + t (as 13m is middle of amplitude, and the time for 12m-13m is t), and at low tide, from 8-13m, when it rises again from 8m to 13m it will be 6.25h + t?

so overall its 2(6.25h + t) = 12.5h + 2t?

does that sound correct? Is my thinking of simple harmonic motion accurate when I assume that for exactly half the time (12.5h) the water level rises and falls at a constant rate from 13m-18m, and 8m-13m?

so overall its 2(6.25h + t) = 12.5h + 2t?

does that sound correct? Is my thinking of simple harmonic motion accurate when I assume that for exactly half the time (12.5h) the water level rises and falls at a constant rate from 13m-18m, and 8m-13m?

If t is the time from a height of 12m to 13m then yes, that is correct.

Incidentally though, the water level NEVER rises or falls at a constant rate, but it will take the same time to rise and fall.

Reply 7

9 years ago

Original post by brianeverit

If t is the time from a height of 12m to 13m then yes, that is correct.

Incidentally though, the water level NEVER rises or falls at a constant rate, but it will take the same time to rise and fall.

Incidentally though, the water level NEVER rises or falls at a constant rate, but it will take the same time to rise and fall.

ah ok, so can you explain how they worked out total time as 12.5 + 2t then please?

Reply 8

9 years ago

Original post by Coral Reafs

ah ok, so can you explain how they worked out total time as 12.5 + 2t then please?

The period of the s.h.m, i.e. the time from the mid-point to one extreme and back to the mid-point again is 12.5. time from 12m to 13m and from 13m back to 12 m is t each time so total time is 12.5+2t.

Reply 9

9 years ago

Original post by brianeverit

The period of the s.h.m, i.e. the time from the mid-point to one extreme and back to the mid-point again is 12.5. time from 12m to 13m and from 13m back to 12 m is t each time so total time is 12.5+2t.

thanks so much for that! +1

btw can you check out my other post please, and see if you can offer some advice? its here

http://www.thestudentroom.co.uk/showthread.php?t=2681826

Thanks!

Reply 10

3 weeks ago

A partical describe of a given arc hyperablic orbit

- Year 2 math content in AS Further Mechanics 2
- How to be good at A-Level Maths Mechanics?
- is aqa physics alevel paper 1 entirely AS stuff?
- Gcse and A level results
- Resonance Concept
- 3rd A-level option
- Possible to self-study 3 A levels in 160 days/5 months?
- Advanced Higher Mechanics
- UCAS Clearing 2023 FAQ and Help Megathread
- Got a Ucas or results related question? Ask a Clearing and Applications Advisor here
- Physics A Level unit 4 questions
- AQA A-Level Physics Paper Topics
- Further maths A level
- Can I use physics formulas in A-level Math?
- Simple Harmonic Motion
- A-Level Computer Science NEA Project Ideas for Engineering?
- SHM
- Further Maths for Civil Engineering
- doing physics a level outside of school
- a =w2x prove it pls

- GCSE Mathematics Study Group 2023-2024
- Hypothesis Testing
- Step support programme assignment 7 help pls
- Senior Maths Challenge 2023
- A-level Mathematics Study Group 2023-2024
- Dimensional Analysis
- Do we have to memorise all physics equations for GCSE 2024 ?
- Girls Maths Olympiad 2023
- Electrical Engineering maths help with Desmos graphing calculator
- A Level Maths Moments question
- Discrete maths questions
- Plotting data on a graph.
- Hypothesis Testing
- Problem solving the smc 2023
- Maths trig
- Help With A level Trig
- which calculator; the fx-991cw or fx-991ex
- AS Maths edexcel 2023
- Edexcel AS Stats and mechanics paper 2023?
- Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong

- Thoughts on the current situation between Palestine and Israel?
- Official: Kent and Medway Medical School A100 2024 entry
- ATAS certificate for UK for January 2024 intake
- Architecture Applicants 2024
- glasgow offer
- Ninja food processor dishwasher safe
- Who did you play in the school nativity?
- The Russell Group hurt/heal game (Part 5)
- Official: University of Cambridge A101 Applicant and Offer Holder thread 2023 Entry
- A-level Arabic (Edexcel)

- Official: University of East Anglia (UEA) A100 2024 Entry
- Personal statement: Biological sciences
- Pharmacy URGENT!!!!!!!!!!!!!!!
- Should I call work and say I'm Sick?
- Diageo graduate scheme
- Can I evict myself from halls
- Should I return for S6 or go to college?
- accounting notes
- Cambridge Parents Association
- Girls Vs. Boys (Part 45)

- Monarchists vs Republicans
- Make your prediction: Will it SNOW this christmas?
- I'm planning to steal Christmas....AMA!
- Psychology, mental health / coaching job advice
- EY 2024 Graduate Program
- Dwp work coach september 2023 merseyside
- The Official Cambridge Applicants for 2024 Entry Thread
- The daily Wordle puzzle thread!
- Official Year 11 Chat 2023-24
- Could I quit my work to do this

- missed catchup work
- University of Oxford 2024 Undergraduate Applicants Official Thread
- is it selfish of me
- Official Imperial College London Offer Holders Thread for 2024 entry
- Can I go to uni through Ucas points if i do 1 btec and 2 alevels
- what is major pros of to get verification information more then more
- Christmas Countdown
- MU123 to prep for M05 Astrophysics
- Motivating myself - my GYG blog :)
- Sevenoaks waitlist

The Student Room and The Uni Guide are both part of The Student Room Group.

© Copyright The Student Room 2023 all rights reserved

The Student Room and The Uni Guide are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: Imperial House, 2nd Floor, 40-42 Queens Road, Brighton, East Sussex, BN1 3XB