Simple Harmonic Motion question (1 Viewer)

[member 6003]

On a certain day, the depth of water in harbour at high tide at 5 am is 9 metres. At the following low tide at 11:20am the depth is 3 metres, Find the latest time before noon that a ship can enter the habour if a minimum depth of 7.5 metres is required.

I keep messing this up idk why.

 

[nathanzhou1234]

a common mistake is that people count the time between the high and low tide as one period - its half a period

 

[yanujw]

We are analysing SHM that begins at the maximum value and then begins to decrease. We can model this using a cos graph.
Period = 12h40m = 38/3 hours.
n = 2pi/(38/3) = 3pi/19
Range = 6m, therefore amplitude (a) = 3m
The centre of motion is 6m so c = 6
Setting 5am to t=0, then the value of alpha in the SHM equation is 0.

So the depth of the water t hours after time t is

Since the depth required is 7.5m, you should arrive at

Taking the first positive solution ->

t = 19/9, giving an answer of 7:08am as the latest time for which the depth is above 7.5m.