Many phenomena can be modeled as simple harmonic oscillation. for instance, consider water level at a certain beach on a certain day.

suppose high tides occur at 8: 00am and 8: 00pm, at which times the water level is 1 m above sea level. low tides occur at 2: 00am and 2: 00pm, at which times the water level is 1 m below sea level.

a) write a mathematical expression that would predict the height of the water level at this beach at any time of day i. e., as a function of time t since midnight).

b) find the times in the day when the ocean level is exactly at sea level.