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Tides The Bay of Fundy in Nova Scotia has the highesttides in the world. In one $12-$ h period the water starts atmean sea level, rises to 21 ft above, drops to 21 ft below,then returns to mean sea level. Assuming that the motion ofthe tides is simple harmonic, find an equation that describes the height of the tide in the Bay of Fundy above mean sealevel. Sketch a graph that shows the level of the tides over a12 -h period.

$d(t)=21 \sin \frac{\pi}{6} t$

Precalculus

Chapter 6

Trigonometric Functions: Unit Circle Approach

Section 6

Modeling Harmonic Motion

Trigonometry

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basic question is talking about the tights were they resemble on move in a simple harmonic motion and one with ours, period. The water starts at mean Sea devil on drivers to 1 12 21 feet above, drops to 20 feet below and then goes again to the museum, so we'll have to find an equation. Describe the emotion on toe sketch the graph. So it's mentioned that the period is 12 hours on DDE. Let's try toe. Draw the graph as it stays just enough. Ah, enough sketch off the graph. It stays. That it starts at means it well. So let's consider This is the mean sea level, which is the X axis. Starting from the means available, it rises to 21 feet above. Then it goes down toe 21 feet below the mean sea level. So as if this one is minus 21 on Dhere is 21. Then it returns toe demean syllable. So this is the graph of the function on dhe. It's clearly that the function of the emotion the motion of the object resembles a sign. Careful. So this is tanker Andi. Maximum aptitude is 21 on during our operative is minus the amplitude minus 20 months. So on this is just one period, and here is the 12 hours as one period means it's on tip. It is the time that takes for one cycle to be completed. So now let's right the function. What is the displacement off the water? Or the height of the water equals well that if the function equals y equals a sign Oh, Meg, etc. And this is the original form off these function, since there is no presenter shift or vertical shift. So just a simple form off the simple harmonic motion. Now the amplitude. I mentioned it already that it is equal to 21. Now let me get can be obtained from the period and we know that Omega it's just to buy over the period 12 and this is equals to play over sex. So now just substituting the values in the equation is a 21 sign by over six multiplied by t on This is just D final solution off this a question as well as the graft drive here

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