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Consider the function f(t)= -r< t〈0, with fit (a) Sketch f(t) by hand for-3r 〈 t 〈 3T. (b) Determine the general...
3. Consider the function f(t) = ' π2 , with f(t) = f(t +2r). 0<t<π (a)...
3. Consider the function f(t) = ' π2 , with f(t) = f(t +2r). 0<t<π (a) Sketch f(t) by hand for-3r < t < 3T. (b) Determine the general Fourier Series for f(t). (c) Use MATLAB to plot f(t) and the n = 4 Fourier series representation on the same set of axes for -t<T
Please show all steps with clear hand writing 3. Consider the periodic function defined by sin(x) 0<x< f(r) = and...
Please show all steps with clear hand writing
3. Consider the periodic function defined by sin(x) 0<x< f(r) = and f(x) = f(x + 27). (a) Sketch f(x) on the interval-3r < r 〈 3T. etch fx on the interva (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by sin(x) 0
3. Consider the periodic function defined by f(x) =sin(r) 0 x<T 0 and f(x) f(x+27) (a) Sketch f(x) on the interval -...
3. Consider the periodic function defined by f(x) =sin(r) 0 x<T 0 and f(x) f(x+27) (a) Sketch f(x) on the interval -3T < 3T (b) Find the complex Fourier series of f(r) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by f(x) =sin(r) 0 x
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on th...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a<...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks
3. Consider the function defined by...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t<...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π...
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π 〈 3T. 9 (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π 〈 3T. 9 (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
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...
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x)...
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
1. Consider the function defined by (1 -2, 0 r< 1, f(x) 1 < |x2 (0. and f(r) f(x+ 4) (a) Sketch the graph of f(x...
1. Consider the function defined by (1 -2, 0 r< 1, f(x) 1 < |x2 (0. and f(r) f(x+ 4) (a) Sketch the graph of f(x) on the interval -6,61 (b) Find the Fourier seriess representation of f(x). You must show how to evaluate any integrals that are needed.
1. Consider the function defined by (1 -2, 0 r
3. Consider the function f(t) = ' π2 , with f(t) = f(t +2r). 0<t<π (a) Sketch f(t) by hand for-3r < t < 3T. (b) Determine the general Fourier Series for f(t). (c) Use MATLAB to plot f(t) and the n = 4 Fourier series representation on the same set of axes for -t<T
Please show all steps with clear hand writing
3. Consider the periodic function defined by sin(x) 0<x< f(r) = and f(x) = f(x + 27). (a) Sketch f(x) on the interval-3r < r 〈 3T. etch fx on the interva (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by sin(x) 0
3. Consider the periodic function defined by f(x) =sin(r) 0 x<T 0 and f(x) f(x+27) (a) Sketch f(x) on the interval -3T < 3T (b) Find the complex Fourier series of f(r) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by f(x) =sin(r) 0 x
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks
3. Consider the function defined by...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π 〈 3T. 9 (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π 〈 3T. 9 (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
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...
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
1. Consider the function defined by (1 -2, 0 r< 1, f(x) 1 < |x2 (0. and f(r) f(x+ 4) (a) Sketch the graph of f(x) on the interval -6,61 (b) Find the Fourier seriess representation of f(x). You must show how to evaluate any integrals that are needed.
1. Consider the function defined by (1 -2, 0 r
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