Question

Question 2 The function $f(t)$ is periodic with period $2pi$ and is defined by $f(t) = egin{cases} pi/2 + t, & -pi le t < 0, \ pi/2 - t, & 0 le t < pi, end{cases}$ $f(t + 2pi) = f(t)$. (a) Sketch $f(t)$ in the interval $-3pi < t < 3pi$. [5] (b) Deduce that certain of the Fourier coefficients of $f(t)$ are zero, and specify the reason for this. [3] (c) Obtain the Fourier series for $f(t)$, and write down explicitly the first three terms of the series. [12]

          Question 2
The function $f(t)$ is periodic with period $2pi$ and is defined by
$f(t) = egin{cases} pi/2 + t, & -pi le t < 0, \ pi/2 - t, & 0 le t < pi, end{cases}$
$f(t + 2pi) = f(t)$.
(a) Sketch $f(t)$ in the interval $-3pi < t < 3pi$.
[5]
(b) Deduce that certain of the Fourier coefficients of $f(t)$ are zero, and
specify the reason for this.
[3]
(c) Obtain the Fourier series for $f(t)$, and write down explicitly the first three
terms of the series.
[12]

Question 2
The function f(t) is periodic with period 2pi and is defined by
f(t) = egincases pi/2 + t, -pi le t < 0, pi/2 - t, 0 le t < pi, endcases
f(t + 2pi) = f(t).
(a) Sketch f(t) in the interval -3pi < t < 3pi.
[5]
(b) Deduce that certain of the Fourier coefficients of f(t) are zero, and
specify the reason for this.
[3]
(c) Obtain the Fourier series for f(t), and write down explicitly the first three
terms of the series.
[12]

Added by Eric G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

Since the function is periodic with period 2T, we can plot it for the interval -T < t < T and then repeat it. For -T < t < 0, f(t) = T/2 + t, which is a straight line with slope 1 and intercept T/2. For 0 < t < T, f(t) = T/2 - t, which is a straight line with Show more…

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The function f(t) is periodic with period 2π and is defined by f(t) = { π/2 + t, -π ≤ t < 0; π/2 - t, 0 ≤ t < π; f(t+2π) = f(t). (a) Sketch f(t) in the interval -3π < t < 3π. (b) Deduce that certain of the Fourier coefficients of f(t) are zero, and specify the reason for this. (c) Obtain the Fourier series for f(t), and write down explicitly the first three terms of the series.