Engineering Mathematics (2) Homework #2 Due date: 23:59 9 Apr. 2020 1. Find the eigenvalue and...
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform 2. tan" G) 3. Check the existence of the Laplace transform for the given function and hence she that -02:49 in 133+ 4 S- where LF(t)) is represent the place transform of (1) [Hint: 2 cos Acos B = (A-2).sin(A+B) + sin(A - m = sin cos sin(A + B) - Sin(A) = 0 4. Find the Fourier Sine series of f(x) <rci 5....
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...
Check the existence of the Laplace transform for the given function and hence show that - cos 20 1s² + 4 L = In t s2 where L{f(t)} is represent the Laplace transform of f(t). [Hint: 2 cos A cos B = COSIA+B) + cos(A - B) sin(A + B) + sin(A - B) = sinA cosB, sin(A + B) – sin(A - ?) = os AsmB] [2+ Find the Fourier Sine series of [8 f(x) = e-*,0<x<. Using the...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
Problem 1. Find the Fourier series expansion of a half-wave rectified sine wave depicted below. AS(0) Answer: f(t) = 1+sin at cos2nt 1 nr 15 2 Cos 4t -cost + ... 35 Problem 2. Find the Fourier series approximation of the following periodic function f(x), where the first two leading cosine and sine functions must be included. Angle sum formulas for sine / cosine functions f(x) sin(A + B) = sin A cos B + cos A sin B sin(A...
Find the Fourier transform of f(x) = 1–x?, for -1 < x < 1 and f(x) = 0 otherwise. Hence evaluate the integral 6 * * cos sin cos des.
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
mechanical engineering analysis help, get from problem to solution, pls show all work, thanks. Problem 2. Find the Fourier series approximation of the following periodic function f(x), where the first two leading cosine and sine functions must be included. f(x) Angle sum formulas for sine / cosine functions sin(A + B) = sin A cos B + cos A sin B sin(A – B) = sin A cos B – cos A sin B TT cos(A + B) = cos...
3.10. Without explicitly solving for X (2), find the ROC of the z-transform of each of the following sequences, and determine whether the Fourier transform converges: (a) x[n] = [(y)"+(!)"]u[n – 10) J1, -10 <n<10, (b) xin] = 1 o. otherwise, (c) x[n] = 2"u[-n] (d) x[n] = |()*++ - (ja/331]u[n - 1] (e) x[n] = a[n+ 10] – u[n+ 50 (f) x[n]=()” [1] + (2+36)-24 – – 1).
(2) Consider the function f(x)- 1 (a) Find the Fourier sine series of f (b) Find the Fourier cosine series of f. (c) Find the odd extension fodd of f. (d) Find the even extension feven of f. (e) Find the Fourier series of fod and compare it with your result -x on 0<a < 1. in (a) (f) Find the Fourier series of feven and compare it with your result in (b)