Question

solve by matlab

The damping system has a single degree of freedom as follows: dx2 dx mo++ kx = F(t) dt dt The second ordinary differential equation can be divided to two 1sorder differential equation as: dx dx F C k xí -X2 -X1 dt dt m m m = x2 ,x'z m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [00] and the time interval is from 0 to 24 with 0.01 increment. Plot time [s] with the displacement x. Show all the details on your plotting M > F(t) 있 Figure [1]. Damping System

Answer 1

clc;clear all;close all;
T=0:0.01:24;%time 0 to 24sec with the increment of 0.01
m=5;k=40;c=0.1;F=10;
fun=@(t,x)[x(2);(F/m)-(c/m)*x(2)-(k/m)*x(1)];%first order differential euation function
IC=[0;0];%initial condition
[t,y] = ode45(fun,T,IC);
%ploting
plot(t,y(:,1));
xlabel('time in sec')
ylabel('Displacement in m')

0.5 0.45 0.4 0.35 0.3 Displacement in m 0.25 0.2 0.15 0.1 0.05 5 20 25 10 15 time in sec