second order differential equation with variable coefficients

I have to solve this differential equation: m*d^2x/dt^2 +k*x= F(x) where F(x) is known for points

Answer 1

[Torsten]

Write your equation as a first-order system

y1'=y2
y2'=(-k*y1+F(y1))/m

use "interp1" to interpolate F(y1) from your known values and call "ode45" to solve.

Best wishes

Torsten.

Answer 2

[Giuseppe Esposito]

Thank you for your answer, I have written the algorithm in this way but it doesn't work

clc; close all; clear all;

xx=[0,2,4,6,8,10,12];

F=[0.65,0.75,0.80,0.81,0.80,0.50];

tspan=[0,0.1];

x0=[0,0];

Fc=@(x) interp1(xx,F,x);

m=15E-3;

k=50;

function dxdt=myfun(t,x,m,k,Fc);

dxdt(1)=x(2);
dxdt(2)=(-k*x(1)+Fc(x(1)))/m;
end

[t,x]=ode45(@(t,x) myfun(t,x,m,k,Fc),tspan,x0);

Answer 3

[Giuseppe Esposito]

I've solved, xx and F hadn't the same length.

Thank you.

[Torsten]

... and dxdt has to be a column vector:

function dxdt=myfun(t,x,m,k,Fc);
dxdt=zeros(2,1);
dxdt(1)=x(2);
dxdt(2)=(-k*x(1)+Fc(x(1)))/m;
end

Best wishes

Torsten.