Simple Harmonic Motion (1 Viewer)

[michaeljennings]

On a particular day, the low tide mark on a wharf was 4.2 metres below the edge of the wharf. Low tide occurred at 9am. The hide tide mark was 1.4 metres below the edge of the wharf and high tide occured at 3:05pm. A boat, tied to the wharf had a deck which was 2.6 metres above water level. Assuming that the rise and fall of the tide is in SHM at what times during the afternoon was the deck exactly level with the wharf?

Could someone show me how to do this question

EDIT: Answer is 12:19pm and 5:51 pm

 

[HyperComplexxx]

do you have the answers?
i got 11:46 am and 6:24pm
If that's right I'' post up what i did

Edit:
Find period first T = 2 X (3:05pm - 9am) = 730min
T = 2 /n
n = /365
Then you draw the motion out
1.4m
2.8m
4.2m
then you get a negative cos graph if you take 2.8m as centre of motion and amplitude = 1.4m
x = -acos(nt + )
t = 0, x = -1.4m
-1.4 = 1.4cos(n(0) + )
then you get = 0
x = -1.4cos(nt)

so you want the boat be right above water level so the water level have to be 2.6m below which equals to 0.2m on the graph
0.2 = -1.4cos(nt)
you got n already so solve for t
t = 199min = 3 hour 19min
T - t = 730 - 199 = 531 = 8 hour 51min
then add those time to your intial time at low tide (9am)
12:19pm and 5:51pm ?

 

[islam10]

that's wrong.

 

[michaeljennings]

answers are up

 

[HyperComplexxx]

there you go

 

[Hermes1]

posting solution in a second......

 

[Hermes1]

wait the guy already did it.

 

[michaeljennings]

hahaha yeah thanks anyway bro

 

[Hermes1]

do you have the answers?
i got 11:46 am and 6:24pm
If that's right I'' post up what i did

Edit:
Find period first T = 2 X (3:05pm - 9am) = 730min
T = 2 /n
n = /365
Then you draw the motion out
1.4m
2.8m
4.2m
then you get a negative cos graph if you take 2.8m as centre of motion and amplitude = 1.4m
x = -acos(nt + )
t = 0, x = -1.4m
-1.4 = 1.4cos(n(0) + )
then you get = 0
x = -1.4cos(nt)

so you want the boat be right above water level so the water level have to be 2.6m below which equals to 0.2m on the graph
0.2 = -1.4cos(nt)
you got n already so solve for t
t = 199min = 3 hour 19min
T - t = 730 - 199 = 531 = 8 hour 51min
then add those time to your intial time at low tide (9am)
12:19pm and 5:51pm ?

ur answers are correct but alpha should hav been equal to pi

 

[HyperComplexxx]

ur answers are correct but alpha should hav been equal to pi

woops, forgot -ve infront of 1.4cos(n(0) + )