Compute the necessary values/derivatives of at
:
Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) at
by
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Another way of doing this would be to solve for the coefficients in
by expanding the right hand side and matching up terms with the same power of .
Answer:
a)
b)
Step-by-step explanation:
Part a
Since the buoy oscillates in simple harmonic motion the equation to model this is given by:
For this case from the info given we know that:
"It returns to its high point every 10 seconds." That means period =10 , and the angular frequency can be founded like this:
Assuming that the value for the phase is our model equation is given by:
Part b
From definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this: