Question

using matlab

The damping system has a single degree of freedom as follows: dx2 dx m++ kx = + kx = F(t) dt dt The second ordinary differential equation can be divided to two 1st order differential equation as: dx dx F с k x1 = = x2 ,X'2 X2 -X1 dt dt m m m m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [0 0] 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. 24 M → F(t) Figure [1]. Damping System

Answer 1

clc
Clear all
F = @(t,x)[x(2); 2-0.02*x(2)-8*x(1)]; 
ic= [0; 0];            % Initial Conditions
ts = [0:0.01:24];                   % Time span
[t,z] =ode45(F,ts,ic);          % Solving through ODE45
plot (ts,z(:,1));    
xlabel('time(t) in s')
ylabel('displacement(x) in m')

0.5 0.45 0.4 0.35 0.3 displacement(x) in m 0.25 0.2 0.15 0.1 0.05 ол Н 0 20 25 10 15 time(t) in s

xi= da व - 2 ㅠ 월 K 이 걸 m m 21 M) 10 5 일기 GO 5 지 5 기 2 - 0.0812 - 8 X) F = @(x) [x(2), 2-0·02 * x(2) - ?* ( N