题目
题目

AMME2000 BMET2960 BMET9960 (ND) Week 4 Pre-work

单项选择题

Open the Fourier Series Demo and select the "Sinusoid" function. The reason the Fourier series representation (shown in green) and analytical representation (shown in red) overlay exactly when the the number of Fourier terms is ≥ 2 is because:

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标准答案
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思路分析
Let’s unpack what the question is saying about the Fourier Series Demo and the overlay of the green (Fourier) and red (analytical) representations. The provided statement asserts that the analytical function is a mode 2 sine wave, and therefore the Fourier representation matches exactly once the number of Fourier terms n is at least 2. First, recall that a Fourier series represents a periodic function as a sum of sine and cosi......Login to view full explanation

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类似问题

Suppose 𝑥 ( 𝑡 ) is periodic with a period of 2, and one period is described by 𝑥 ( 𝑡 ) = 𝑒 − 𝑡 for − 1 < 𝑡 ≤ 1 . Which of the following is the correct form of the Fourier series coefficients? Note: The hyperbolic sine function is defined as sinh ( 𝑥 ) = 1 2 ( 𝑒 𝑥 − 𝑒 − 𝑥 ) .

In the Fourier series expansion of the even function f(x), the cosine coefficients 𝑎 𝑛  are equal to zero.

In the Fourier series expansion of the even function f(x), the cosine coefficients  are equal to zero.

Open the Initial Condition Demo and select any of the curves defined on the interval [ 0 , 𝐿 ] . Now toggle between 'Even' and 'Odd' to extend this curve as an even or odd function, respectively, on the interval [ − 𝐿 , 𝐿 ] . Which of the following statements is true?

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