Code
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clc;clear;
syms t;
i = 1;
for t = -4:1:4
h(i) = exp(-t)*(heaviside(t)-heaviside(t-1));
x(i) = sin(2*pi*t/8)*(heaviside(t)-heaviside(t-4));
i = i + 1;
end
y_t = conv(x,h);
plot(y_t)
grid on
title 'Convolution'
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1. Find the output, if, 2Ttt ho)-(u()-u(t -)andx(t) sin((t)-u(t -4) and plot the Sin(_ result Also...
FInd u(x,t) and lim u(x,t) Solve the heat problem Ut = Uzx + 5 sin(4x) - sin(2x), 0 < x <7, u(0,1) = 0, u(,t) = 0 u(x,0) = 0
(1 point) Solve the nonhomogeneous heat problem Ut = uzz + 4 sin(5x), 0< I<T, u(0, t) = 0, u(T, t) = 0 u(x,0) = sin(3.c) u(x, t) = Steady State Solution lim, , u(x, t)
(1 point) Solve the nonhomogeneous heat problem u, = Uxx + 5 sin(5x), 0<x<1, u(0,t) = 0, u1,t) = 0 u(x,0) = 4 sin(4x) u(x, t) = Steady State Solution lim 700 u(x, t) =
Find the following trigonometric limit: lim sin - Hint the substitution [((u-1)E)s01 u= t-n makes life 1. tm easier. Work inside the [...] first and then take the sine of your result, that is, use the rule that allows you to take the limit inside the sine function: lim sin(f(x)) n(Hm/s) sin x-a 2. Use the results we derived in class for power functions to find the derivative of g(x) (3x4 + v 4 atx Ans 3. When a function...
1. (A) Use the Taylor series expansion for the sin x to estimate sin(t/4) for the acceptable relative errors of 0.25 and 0.0025 .5 3 9 х* sin x x 3! х> 5! 7! 9! Please use the table formatting u to solve the problem
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
(1 point) Solve the nonhomogeneous heat problem u; = Uxx + 4 sin(5x), 0 < x < t, u(0, t) = 0, u(1, t) = 0 u(x,0) = 2 sin(2x) u(x, t) = Steady State Solution limt700 u(x, t) =
In MATLAB Use symbolic math to solve and plot Laplace Problem 3.5. Problem 3.5 x1(t) 16e2t cos4t u(t x2(t) 20te2t sin4t u(t) x3(t) 10e 3t ut-4) a. b. C. In MATLAB Use symbolic math to solve and plot Laplace Problem 3.5. Problem 3.5 x1(t) 16e2t cos4t u(t x2(t) 20te2t sin4t u(t) x3(t) 10e 3t ut-4) a. b. C.
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t) + 2t sin (2na:) , 0 < x < 1, 0, u(1,t)=0, t > 0, sin(2π.r)-5 sin (4π.r) , 0 < x < 1. t > 0, = = = 4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t)...
(1 point) Solve the nonhomogeneous heat problem 24 = 1,+ sin(2.0), 0<I<T, u(0,t) = 0, u1,t) = 0 u(3,0) = 3 sin(4x) uz,t) = sinx, sint Steady State Solution limuz,t) =