Which pair of functions below cannot be a fundamental set of solutions? And then explain/show why...
6. Which pair of functions below cannot be a fundamental set of solutions? (8 Puan) 5e + 5, 2e + 2 e-21, te-21, 5 cost + 3 sint , 3 cost + sint e2%, cos 2x + sin 2x O1, x2, x2 In x
Differential equations / which pair of functions below
cannot be a fundrmental set of solutions?
6. Which pair of functions below cannot be a fundamental set of solutions? (8 Points) 1, x3, xinx 3 cost + 6 sint, 5 cost + 10 sint €2x cos 3x + sin 3x, 1 e-31 3 te-31 5et + 5, 2e + 1
6. Which pair of functions below cannot be a fundamental set of solutions? (8 Puan) 3 cost + 6 sinr. 5 cost + 10 sin ? ex cos 3r + sin 3r. 1 50+5, 24+ 1 e-34, te 34 Inc
6. Which pair of functions below cannot be a fundamental set of solutions? * (8 Puan) O 1, x, x? Inx O 5e + 5, 2eX + 1 0 2x, cos 3x + sin 3x, 1 3 cost + 6 sint , 5 cost + 10 sint O e-31, te-31
Problem 1a. Verify that the given functions form a fundamental set of solutions of the differential equation. 4y'' + 36y = 0; y1 = cos(3x); y2 = sin(3x)
Find 1d. (LT = Laplace Transforms) use the function:
>>pretty(laplace(exp(-a*t)*cos(b*t)))
For la – d, find the LTs of the functions by hand, and then use MATLAB to verify the LTs. Include your hand calculations and your MATLAB script for the report. la) 2e-3t + 4te-5t + 6t2 b) 7e-atu(t – 2) c) t(sin(wt)) d) t-e-at
Please show step-by-step solution and explain. Thanks!
For each one of the following functions of t, indicate whether they are periodic or not. If periodic, indicate its period, and if not periodic, indicate why. Assume n is a positive integer. Sin (b) sin (xt) +cos (V3t) (c) sin ( 쭉 ) + cos (2nt) + sin ( 2F) + sin( (d) cos (2nt) (e) cos (xt) - cos (t) (f) sin (nt) cos (2nt) )
Please show solutions.
Answer:
1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
7.1-12. Determine which of the following functions can and cannot be valid power density spectrums. For those that are not, explain why. (a) 06 +302 +3 (b) exp[-(0-1)?] 04 (0) 360) (1 + 0 + 0* +1 7.1-13. Work Problem 7.1-12 for the following functions: (a) cos(30) (b) — 1 ” (1 + m2)2 1+02 - (d) T (d) TI-30² (c) lol 1+20 +02 N u ore la is a set of real constants and the processes