Question

Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs. Solve the equation and hand-plot (on the next page) two displacement curves y(t) and x(t) as a function of time t. 1, (10%) write (copy exactly) the Matlab Command here:

Answer 1

MATLAB code is given below in bold letters.

main MATLAB script file code:

clc;
close all;
clear all;

% define the Ode solver as given below
[t,y] = ode23(@vdp1,[0 20],[0 ; 0]);
% Plot the solutions for and against t.

figure;plot(t,y(:,1),'-o',t,y(:,2),'-o')
title('Solution with ODE23');grid;
xlabel('Time t');
ylabel('Solution');
legend('position','velocity');

functionn file code:

function dydt = vdp1(t,y,mu)

% define the parameters as follows
m = 1;
c = 1;
k = 3;
f = 10;

% define the first order state space differential equations as given below
dydt = [y(2); 1/m*(-k*y(1)-c*y(2) + f)];

Result: