Question

1. 1i3 points | Previous Answers My Notee Aek Your Teacher 11 6.3.001 The given differential equation is a model of an undamped spring/mass system in which the restoring force Fix) in (1) md2+ dr (x) = 0 (1) is nonlinear. For the equation use a numerical solver to plot the solution curves that satisfy the given initial conditions. xit) xit) xi2) xt4) 0.5 If the solutions appear to be periodic, use the solution curve to estimate the period T of oscillations. (If the solution curve is not periodic, enter NOT) period for x(0) = 1, x'(0)-1 period for x(0)- , x'(0)--1 | 11.2

Answer 1

MATLAB Code:

close all
clear
clc

% x'' = -x^3
% x' = x1
% x1' = -x^3

[t, x] = ode45(@vdp, [0 20], [1; 1]);
figure, hold on
grid on
plot(t, x(:,1))
[t, x] = ode45(@vdp, [0 20], [1/2; -1]);
plot(t, x(:,1))
title('Solution Curves'), xlabel('t'), ylabel('x(t)')
hold off

function dxdt = vdp(~, x)
% x(1) => x, x(2) => x1
dxdt = [ x(2);
-x(1)^3];
end

Plot:

Solution Curves X: 6.182 Y: 0510

For first graph (first set of initial conditions): Period is 5.6 approximately.

For second graph (second set of initial conditions): Period is 6.2 approximately.