This will become clear from the resolution of the other thread, which is essentially the same question.Veronica_Oles said:Homework Statement
The function h(t) = 5 sin (30(t+3)) is used to model the height of tides. On a different day, the maximum height is the minimum height is -8 and high tide occurs at 5:30am.
Modify function so it matches new data.
Homework Equations
The Attempt at a Solution
Answer: h(t) = 8 sin (30(t-2.5))
I know how to get the 8 b/c (8-(-8))/2 = 8
But I don't understand where the 2.5 comes from?
You take 360 divide it by the period then get k value?haruspex said:This will become clear from the resolution of the other thread, which is essentially the same question.
Do you understand where the 30 comes from? (It really should be more like 29.)
Yes. What is the period in this case?Veronica_Oles said:You take 360 divide it by the period then get k value?
The period is 12.haruspex said:Yes. What is the period in this case?
Ok, but more accurate is 12.4.Veronica_Oles said:The period is 12.
Okay.haruspex said:Ok, but more accurate is 12.4.
h(t) is the mathematical representation of the tidal height at a specific location over a period of time. It is typically modeled using a sinusoidal function and is influenced by various factors such as the moon's gravitational pull and the shape of the coastline. Tidal data refers to the actual measurements of the water level over time at a specific location.
The frequency of modifying h(t) depends on the rate at which tidal data changes. This can vary depending on the location and the specific tidal patterns observed. In some cases, h(t) may need to be modified on a monthly or even weekly basis, while in other cases it may be sufficient to update it on a yearly basis.
There are various methods that can be used to modify h(t) to match new tidal data. Some common approaches include adjusting the amplitude and phase of the sinusoidal function, adding or subtracting a constant value, or using more complex mathematical models that take into account additional factors such as wind and atmospheric pressure.
Yes, h(t) can be modified to make predictions about future tidal data. This can be done by extrapolating the existing data and trends, or by using more advanced computational methods such as data-driven modeling or machine learning techniques. However, it is important to note that these predictions may not always be accurate and should be used with caution.
Some potential challenges in modifying h(t) to match new tidal data include identifying the most accurate and appropriate mathematical model, dealing with missing or incomplete data, and accounting for unforeseen changes or anomalies in tidal patterns. Additionally, the process of modifying h(t) may also require a significant amount of computational resources and expertise in data analysis.