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please solve both questions
1. The values of a period 21t function f(c) in one full...
Question Help 9.1.13 The values of a period 2π function f(t) in one full period are given. Sketch...
Question Help 9.1.13 The values of a period 2π function f(t) in one full period are given. Sketch several periods of its graph and find its Fourier series. f(t) = Sketch several periods of its graph. Choose the correct graph below A. frt) frt) f(U) -2x 2t -2 -2J 2x 2x Find its Fourier series. f(t) (Type a series using n as the index variable and 1 as the starting index, Type an exact answer, using π as needed. Use...
2. Derive the Fourier series and graph the period 27 function to which the series converges....
2. Derive the Fourier series and graph the period 27 function to which the series converges. (-1)"+1 sin nt t -11 <t<tt 2 n 2 n=1
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selan...
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
Part (c) please 6. (continued) Recall that f: [-7,7] → R is the function ſo if...
Part (c) please
6. (continued) Recall that f: [-7,7] → R is the function ſo if – <r<0 f(0) = { if 0 SIS and its Fourier series is the function F: R R given by (-1)" - 1 FC) = - + 11=1 TTn? cos(not) + (-1)"+1 n sin (n.) (b) Sketch the graph of F. In your sketch, clearly indicate the point (37, F(37)). (c) Does the Fourier series of f converge uniformly on [-27, 2n]? Provide a...
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a...
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm 2rpt @pcos! ㅡ ㅡ l+, bnsin 2mpt p=1 (c) Derive the expression of the steady state response x() of a single degree-of-freedom (DOF) mass-spring-damper system subject to the excitation f(o).
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm...
Let f(t) be periodic function with period T = 1 defined over 1 period as
Let f(t) be periodic function with period T = 1 defined over 1 period as f(t) = {t -1/2 < t < 1/2} (a) Plot f(t) and find its Fourier series representation. (b) Find the first four terms of the fourier series.
4 please In each of Problems 3 to 7 (a) sketch the graph of the given...
4 please
In each of Problems 3 to 7 (a) sketch the graph of the given function for three periods, (b) find the Fourier series, and (c) sketch the graph of the function to which the series converges for three periods. 3. f(x) = -1, -L <r<L; f(x + 2L) = f(x) 4. f(x) = { }; -L<=<0, 0, 052<L: f(x+2L) = f(x) 5. Ls - 1 +1, -13&<0,1 <: (x + 2) = f(x) 0 < 1; ) +...
Find the required Fourier Series for the given function f(x). Sketch the graph of f(x) for...
Find the required Fourier Series for the given function f(x).
Sketch the graph of f(x) for three periods. Write out the first
five nonzero terms of the Fourier Series.
cosine series, period 4 f(0) = 3 if 0<x<1, if 1<x<2 1,
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch...
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch the function over the interval -3m<<3x. [3] (b) Find the cireular frequency a and the symmetry of the function (odd, even or neither). 21 (e) Determine the trigonometric Fourier coefficients for the function f) [10] (d) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. [5] (e) Determine the Fourier series for the function g(t)-2r-1 over the...
Q2. The following function f(t) is periodic with fundamental period To Sketch f(t) for at least...
Q2. The following function f(t) is periodic with fundamental period To Sketch f(t) for at least 2 full cycles and obtain an expression for the Fourier series. Ensure that you calculate all coefficients and check your answer with the knowledge of odd or even functions. (0 – T. /251<-To 14, f(t) = {2A, - T./451< +T./4, 0, +T, / 4<t<+T72.
Question Help 9.1.13 The values of a period 2π function f(t) in one full period are given. Sketch several periods of its graph and find its Fourier series. f(t) = Sketch several periods of its graph. Choose the correct graph below A. frt) frt) f(U) -2x 2t -2 -2J 2x 2x Find its Fourier series. f(t) (Type a series using n as the index variable and 1 as the starting index, Type an exact answer, using π as needed. Use...
2. Derive the Fourier series and graph the period 27 function to which the series converges. (-1)"+1 sin nt t -11 <t<tt 2 n 2 n=1
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
Part (c) please
6. (continued) Recall that f: [-7,7] → R is the function ſo if – <r<0 f(0) = { if 0 SIS and its Fourier series is the function F: R R given by (-1)" - 1 FC) = - + 11=1 TTn? cos(not) + (-1)"+1 n sin (n.) (b) Sketch the graph of F. In your sketch, clearly indicate the point (37, F(37)). (c) Does the Fourier series of f converge uniformly on [-27, 2n]? Provide a...
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm 2rpt @pcos! ㅡ ㅡ l+, bnsin 2mpt p=1 (c) Derive the expression of the steady state response x() of a single degree-of-freedom (DOF) mass-spring-damper system subject to the excitation f(o).
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm...
4 please
In each of Problems 3 to 7 (a) sketch the graph of the given function for three periods, (b) find the Fourier series, and (c) sketch the graph of the function to which the series converges for three periods. 3. f(x) = -1, -L <r<L; f(x + 2L) = f(x) 4. f(x) = { }; -L<=<0, 0, 052<L: f(x+2L) = f(x) 5. Ls - 1 +1, -13&<0,1 <: (x + 2) = f(x) 0 < 1; ) +...
Find the required Fourier Series for the given function f(x).
Sketch the graph of f(x) for three periods. Write out the first
five nonzero terms of the Fourier Series.
cosine series, period 4 f(0) = 3 if 0<x<1, if 1<x<2 1,
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch the function over the interval -3m<<3x. [3] (b) Find the cireular frequency a and the symmetry of the function (odd, even or neither). 21 (e) Determine the trigonometric Fourier coefficients for the function f) [10] (d) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. [5] (e) Determine the Fourier series for the function g(t)-2r-1 over the...
Q2. The following function f(t) is periodic with fundamental period To Sketch f(t) for at least 2 full cycles and obtain an expression for the Fourier series. Ensure that you calculate all coefficients and check your answer with the knowledge of odd or even functions. (0 – T. /251<-To 14, f(t) = {2A, - T./451< +T./4, 0, +T, / 4<t<+T72.
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