The periodic function so(t) with period 16 given by so(t) = 0 1 10 if –...
The periodic function so (t) with period 28 given by 0 if-14 t<-2.5 80(t) = 〈 1 if _ 2.5 t < 2.5 0 if 2.5 t<14. has the Fourier series defined by So(0) = 0.178571 0 and for n 0.178571* sin(nT5/28) nT5/28 $(n) = Use linearity and the shifting property to find the Fourier Series fors(t), defined by 0 if -14st<-1 0 if9 St<14. S(0)- and for n S(n) 0
The periodic function so (t) with period 28 given...
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 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...
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...
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 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.
A function is defined over (0,6) by 0 <and I <3 f(1) = - { 3<; and <6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. N y 1 0 -10 5 5 10 15 X The function may be approximated by the Fourier series f (t) = a0 + 1 (an cos (021 ) + bn sin ( 122 )), where L is the half-period of the function. Use...
Given the periodic function 5 f(1) = { 1 f (+4) 0<i and I<2 2 <r and I<4 otherwise and its graph is displayed below. 6 5 4 y 3 2 1 0 -2 2 4 6 00+ x The function may be approximated by the Fourier series f(t) = 40 + 1 (an cos ( 172 ) + bn sin where L is the half-period of the function. + bn sin ne :)), L Calculate the coefficients of the...
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]
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.