NOTE: I need the correct answer with every single details
The given differential equations are
Taking Laplace transform of equation (1), we get
Since , we get
Taking Laplace transform of equation (2), we get
Since , we get
Substituting for X1(s) from equation (4) in equation (3), we get
Substituting for X2(s) from equation (5) in equation (4), we get
Taking the inverse laplace transform, we get
The plots of and are shown below
MATLAB CODE
% For inverse laplace transform
syms s
D = (((s^2)+5)*((s^2)+2)*(s+1))-(4*(s+1));
X1 = (2*((s^2)+2))/D;
X2 = 4/D;
x1 = ilaplace(X1)
x2 = ilaplace(X2)
% For plotting
clear
t=0:0.1:10;
x1=zeros(length(t),1);
x2=zeros(length(t),1);
for i = 1:length(t)
x1(i)=(3*exp(-t(i)))/7 - (8*cos(6^(1/2)*t(i)))/35 - cos(t(i))/5 +
sin(t(i))/5 + (4*6^(1/2)*sin(6^(1/2)*t(i)))/105;
x2(i)=(2*exp(-t(i)))/7 + (4*cos(6^(1/2)*t(i)))/35 - 2*cos(t(i))/5 +
2*sin(t(i))/5 - (2*6^(1/2)*sin(6^(1/2)*t(i)))/105;
end
figure (1)
plot(t,x1,'-r')
hold on
plot(t,x2,'-g')
grid on
xlabel ('time (s)');
ylabel ('x_{1}(t),x_{2}(t)')
legend ('x_{1}(t)','x_{2}(t)')
title ('Time response')
NOTE: I need the correct answer with every single details The two coupled differential equations: *1...
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform method: Xy-=5x1-2x2 + Mu(t-1) x2-=-2x1 + 2x2 x,(t) and x2(t) refer to the motions of the two masses. Consider these initial conditions: x1 (0) = 1, x; (0)-0, x2(0) = 3, x(0) 0 Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system...
1. [-/1 Points] DETAILS CHENEYLINALG2 1.1.001. MY Solve this system of equations and verify your answer. (If the system is inconsistent, enter INCONSISTENT.) 2x2 – 3x3 = -10 4x1 + x2 + 3x3 47 5x3 = 40 (x1, x2, x3) 2. [-/1 Points] DETAILS CHENEYLINALG2 1.1.002. MY Solve this system of equations and verify your answer. (If the system is inconsistent, enter INCONSISTENT.) 3x1 = 2x1 6 5x2 + 6x3 = -35 + 5x3 = -28 - 4X1 (x1, x2,...
[-/1 Points] DETAILS ROLFFM8 2.2.048. - Solve the following system of equations by reducing the augmented matrix. X1 X2 + 6x3 = -2 8X1 + X2 + 8x3 8.5 2x1 + 2x2 + X3 = 3.5 (X1, X2, X3) = Need Help? Watch It Talk to a Tutor
[-/1 Points] DETAILS ROLFFM8 2.2.052. Solve the following system of equations by reducing the augmented matrix. X1 + 3x2 - x3 + 2x4 -3 - 3x1 + X2 + x3 + 3x4 = -2 2x3 + X4 = - 4x4 = -6 2X1 4x2 2X2 1 (X1, X2, X3, X4) = D) Need Help? Talk to a Tutor
I'm trying to solve this differential equations by using matlab. But I don't know the reason why I can't get the solutions. I've attached matlab code and few differential equation. Please find a the way to solve this problem. second oder ode2.m x+ function, second-oder-ode2 t-0:0.001:30 initial-x = 0; initial-dxdt = 0: lt.影=ode45( @rhs, t, [initial.x initial.dxdt ] ); plot(t.(:,1l): xlabel( t); ylabel(x): 申 function dxdt=rhs( t, x) dxdt-1 =x(2); dxdt-2 (-50 x(2)+61.25+((1-cos(4 pi 10 t))/2) (47380 x(1)-3-7428 x(1) 2...
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibits stable oscillatory behavior. Van der Pol realized the parallel between the oscillations generated by this equation and certain biological rhythms, such as the heartbeat, and proposed this as a model of an oscillatory cardiac pacemaker. Solve the van der Pol equation using Second-order Runge Kutta Heun's method with the...
please help me with this MATLAB CODE and explain to me what each line does and what is used for? leave your comments as words, not as pictures. ..................................................................................................................................................................... clear all; close all; % For a script file, you better start with clear all and close all % However, for a fucntion, you better NOT to start % with them %% End of cell mode example %% Plot function t = 0:0.1:5; x1 = sin(2*5*t); x2 = cos(3*7*t);...
need help all those questions. 10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...
(2-2) Problem 1, 12 points Let A and consider the system of differential 1 -2 equations y' = Ay. kx a) Find the characteristic polynomial of A b) Use the Laplace transform method to compute eAt. c) Solve the system y - Ay, 0)o
Only need the last question 5 thanks! 3) RLC Parallel Circuits: Differential Equations and Laplace U2 U1 TOPEN 0 TCLOSE 0 L1 R1 0.15H C1 2E-8F 11 10E-3 2 10E-3 At t 0, U1 closes and U2 opens. 3.1: What is the intial (t-0+) current through the capacitor? What is the initial (t=0+) voltage across the capacitor? 3.2: What is the DC steady state current though the capacitor ast goes to infinity? 3.3: Find the current through the CAPACITOR as...