Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0 Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...
(USING MATLAB) Given two differential equations X= sin(t)(exp(cos(t))-2cos(4t)+sin(t/12)^5) And Y = cos(t)(exp(cos(t))-2cos(4t)+sin(t/12)^5) where 0<t<20pi is a vector of 5000 points created by using (linspace) command : Write script to plot X and Y with red color ?
1291) Determine the Inverse Laplace Transform of F(s)=(18s + 3)/(s^2+20s+164). The answer is f(t)=A*exp(-alpha*t)*cos(w*t) + B*exp(-alpha*t)*sin(w*t). Answers are: A,B,alpha,w where w is in rad/sec and alpha in sec^-1. ans:4
Find the derivative 1.) X(+) = cos(+²) 2.) X(t) = cos(( exp (-+)7²) 3.) × (t) = cos(-exp (+²) 4.) X(t) = cos (exp(+²)) sin(t) s.) X(t) = cos (cos(+)) exp(-t)
Problem 7 If A cos 0,+B sin oft = rsin(0 -0) = R cos(t-8), (a) determiner and in terms of A and B , and (b) the relationship among R,r, 8 and 2 Ans. (a) r = VA’ + Bº, tan 0 4 b)r=R, 0 = 8-5, tan tan 8 +1 = 0 Problem 8 (a) Define the steady state solution of a given SLDE. (b) Consider the motion of a 2-kg mass in a (m,c,k)-system under a cyclic load....
9. Solve - cos(x) for 0 <x < 27, t > 0 ax2 at2 y(0, t) y(27, t) = 0 for t 0 y(x, 0) y(x.0)= 0 for 0 <x < 27. at Graph the fortieth partial sum for some values of the time. 11. Solve the telegraph equation au A Bu= c2- at ax2 at2 for 0 x < L, t > 0. A and B are positive constants The boundary conditions are u(0, t) u(L, t)=0 for t...
2. Let A = (cos, sin and B = (cos, sin) be two vectors on the x-y plane. Let C = (cos, sin be another non-zero vector on the x-y plane not collinear with A or B. Show that Ax B = -Bx C. If we could cancel B, as we could if these were real numbers, is it true that A= -Č? 2. Let A = (cos, sin and B = (cos, sin) be two vectors on the x-y...
Please need answers theta1 and theta2 in degree 900) x(t)- C0 + Cl*sin(w*t+thetal) + C2*sin(2*w*t+theta2) A2*cos (2*w*t) + B2*sin(2*w*t) w-600 rad/sec minus 180 degrees. theta2 (deg) ans:5 x (t)A0 + Al*cos (w*t) + B1*sin(w*t) + Express all angles between plus and Determine co, c1, thetal (deg), C2, Function Symmetry Even Odd Half-Wave Full-Wave 1) T/2 x(t) 2) x(t) Fill out the table using1's and 0'ts For example, if the first fumction is odd and has full-wave symmetry the top row...
Out98 3 B Cos [3 t -3 B Cos [k t] + Ak Sin [3 t A Sin [k t -9+k2 3 (-9 k2) formulay[t] = yzeroinput [t] + yunforced [t] Step 4: Set In99 clear[formulay]; formulay [t_]= Simplify[yzeroinput [t] yunforced [t]] Ou100 -0.460481 Cos [3 t 3 B Cos [3 t 0.00158575 Sin [3 t] + 3 B Cos [k t + Ak Sin [3 t] (-9 k2) A Sin [k t -9+k2 How does this formula signal that...
2. LetA = 〈cos-, sin? and B = 〈cosi' sin, be two vectors on the x-y plane. Let -(cos-, sin π〉 3 4 be another non-zero vector on the x-y plane not collinear with A or B. Show that A × B =-B × C. If we could cancel B, as we could if these were real numbers, is it true that A =-C? [Show your work and conclusions on a separate sheet of paper] 2. LetA = 〈cos-, sin?...