Thread: Simple Harmonic Motion

Hey guys.
How exactly do I do this question???
The rise and fall in sea level due to tides can be modelled by simple harmonic motion. On a certian day, a channel is 10 m deep at 9 am when it is low tide and 16 m deep at 4 pm when it is high tide. if a ship needs 12 m of water to sail down a channel safely, at what times between 9 am and 9 pm can the ship pass through?.

Originally Posted by UltraGirl

Hey guys.
How exactly do I do this question???
The rise and fall in sea level due to tides can be modelled by simple harmonic motion. On a certian day, a channel is 10 m deep at 9 am when it is low tide and 16 m deep at 4 pm when it is high tide. if a ship needs 12 m of water to sail down a channel safely, at what times between 9 am and 9 pm can the ship pass through?.

Start by defining a clock time for t = 0 and then find a model for the depth. I suggest setting t = 0 at 9.00 am and using the model . Your job is to determine the values of a, b and c. Then solve for t and convert your answer to clock times.

Ummm so I've managed to find that the ship can sail beginning from 11.45 am but I dont get how to get 8.15 pm when the ship can no longer sail (from the answers)

ive found that the equation of motion is x = 13 - 3 cos(pi/7 * t)

and so i let x = 12 and derived t =- 7/pi * arccos(1/3) + 14n where n is an integer...

Originally Posted by UltraGirl

Ummm so I've managed to find that the ship can sail beginning from 11.45 am but I dont get how to get 8.15 pm when the ship can no longer sail (from the answers)

ive found that the equation of motion is x = 13 - 3 cos(pi/7 * t)

and so i let x = 12 and derived t =- 7/pi * arccos(1/3) + 14n where n is an integer...

Draw graph of x = 13 - 3 cos(pi/7 * t) and x = 12 on the same set of axes to see what's happening.

Note that cosine is negative in the second quadrant and the third quadrant ....