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Refer to the figure shown below which illustrates the problem.
Low tides occur at a depth of 2.5 m at 12:00 am and 12:30 pm, separated by a period of T = 12.5 hours.
Likewise, high tides occur at a depth of 5.5 m at 6:15 am and 6:45 pm, separated by a period of T = 12.5 hours.
Use a time coordinate of t hours.
The amplitude is (1/2)*(5.5 - 2.5) = 1.5 m.
Use x(t) to denote depth at time t.
Because x(0)=2.5 and x(T/2) = 5.5,, use the periodic function
Verify the model.
x(0) = -1.5 + 4 = 2.5
x(6.25) = 1.5 + 4 = 5.5
x(12.5) = -1.5 + 4 = 2.5
A computer plot for x(t) is shown in the accompanying figure.
Low tides occur at a depth of 2.5 m at 12:00 am and 12:30 pm, separated by a period of T = 12.5 hours.
Likewise, high tides occur at a depth of 5.5 m at 6:15 am and 6:45 pm, separated by a period of T = 12.5 hours.
Use a time coordinate of t hours.
The amplitude is (1/2)*(5.5 - 2.5) = 1.5 m.
Use x(t) to denote depth at time t.
Because x(0)=2.5 and x(T/2) = 5.5,, use the periodic function
Verify the model.
x(0) = -1.5 + 4 = 2.5
x(6.25) = 1.5 + 4 = 5.5
x(12.5) = -1.5 + 4 = 2.5
A computer plot for x(t) is shown in the accompanying figure.