New Senior Math Simple Harmonic Motion Question

[frog0101]

Hi, in the New Senior Math 4 unit textbook, in question 14 they get 12.47 pm, however I am continuously getting 11:32.5 am.

The question is as follows:
The deck of a ship is 2.4 m below the level of a wharf at low tide and 0.6 m above wharf level at high tide. Low tide is a 8:30 am and high tide is at 2:35 pm. Find the time when the deck is level with the wharf, assuming the motion of the tides is simple harmonic.

Any help, would be much appreciated.

[RuiAce]

Quickly looking at it, you used the value for x that's halfway between high tide and low tide. As high tide is 0.6m above and low tide is 2.4m below, the equilibrium height of the tide is 0.9m below.

i.e.
- Low tide: x=-2.4
- Midpoint: x=-0.9
- High tide: x=0.6

You want when when x=0. Not when x=-0.9
Carefully note that the midpoint of SHM is not when the deck is level with the wharf

[frog0101]

Thanks heaps