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.
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