The periodic function so(t) with period 28 given by 0 if 14t<-3 if3 st< 14. 0 has the Fourier series defined by So(0) 0.214286 and for n 。 0.214286sin(n6/28) nT6/28 So(n) Use linearity and the shifting property to find the Fourier Series for s(t), defined by 0 if 14t<-2.5 2 if 2.5 t <3.5 s(t)- 6 if 3.5 t<9.5 0 if 9.5 <14. S(0) 2.357 and for n 0 The periodic function so(t) with period 28 given by 0 if...
The periodic function so(t) with period 28 given by if 14 t<-0.5 1 if _ 0.5 〈 t < 0.5 so(t)- 0if 0.5 t< 14. has the Fourier series defined by So(0)-0.0357143 and for n 0 0.0357143 * sin(nTl/28) nT1/28 Use linearity and the shifting property to find the Fourier Series for s(t), defined by f -14 t <4.5 -5 if 4.5 t< 5.5 3 if 5.5 t<6.5 if 6.5 < t < 14. s(t) S(0) and for n S(n)...
The periodic function so(t) with period 16 given by so(t) = 0 1 10 if – 8<t< -1 if –1<t<1 if 1 <t<8. has the Fourier series defined by S.(0) = 0.125 and for n +0 So(n) = 0.125 * sin(n72/16) 772/16 Use linearity and the shifting property to find the Fourier Series for s(t), defined by s(t) = O 1-5 4 lo if – 8<t<1 if i<t<3 if 3 <t<5 if 5 <t<8. S(0) = and for n 70...
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...
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.
c) Calculate the symmetric Fourier series for the periodic function f(t) with period 21 defined on the interval [-a, ] below using on = 21, f (t)e- jntdt. f(t) = { 13 - St<0 LO 0 <t<t and calculate the values for c, and c. [10 marks]
The sketch of the following periodic function f (t) given in one period f(t) t2 -1, 0s t s 2 is given as follows f(t) 2 -1 We proceed as follows to find the Fourier series representation of f (t) (Note:Jt2 cos at dt = 2t as at + (a--)sina:Jt2 sin at dt = 2t sin at + sin at. Г t2 sin at dt-tsi. )cos at.) Please scroll to the bottom of page for END of question a) The...
Let f(t) be a 2L- periodic wave function with one period on -pi<= t <= pi defined as f(t) = 1 if |t| <= T and 0 if T < |t| <= pi Find the real fourier series of f(x) first and then convert to complex form
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
please answer both questions 3. A function f(t) defined on an interval 0 <t<L is given. Find the Fourier cosine and sine series of f. f() = 6(1-1),0 <t< 4. Find the steady state periodic solution, *xp(t) of the following differential equation. *" + 5x = F(t), where FC) is the function of period 2nt such that F(t) = 18 if 0 << < 1 and F(t) = -18 if t <t <200.