Page 361 - MATLAB an introduction with applications

346 ——— MATLAB: An Introduction with Applications

Figure E6.3(a) shows the response history.
0.15

0.1

0.05

Displacement(m) –0.05 0

–0.1

–0.15

–0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time(s)
Fig. E6.3(a) Response history

Example E6.4: Solve numerically the solution to the problem of a spring mass system excited by a triangular
impulse. The differential equation of motion and the initial conditions are given as

0.5X + 8π X = F ()
2
t

with X = X = 0
1
1
The triangular force is defined in Fig. E6.4. Use central difference method with ∆t = 0.05 sec.
F(t)

150

50

0 t
0 0.20 0.40
Fig. E6.4
Solution: The following MATLAB program is developed:
% INITIAL VALUES
m=0.5;k=8*pi^2;c=0;dt=0.05;
x0=0;x0d=0;