Example 1

 Example 1: Free vibration without damping
            solve    1/8 u" + 24 u = 0
                     u(0) = 1/6; u'(0) = -1
 

Example 2

Example 2: Free vibration with damping
            solve    u" + 0.125 u' + u = 0
                     u(0) = 2; u'(0) = 0
 
 

Example 3

Example 3: Forced vibration without damping (beat)
            solve    u" + u = 0.5 cos(0.8t)
                     u(0) = 0; u'(0) = 0
 
 

Example 4

Example 4: Forced vibration without damping (resonance)
            solve    u" + u = 0.5 cos(t)
                     u(0) = 0; u'(0) = 0
 
  

Example 5

Example 5: Forced vibration with damping (No resonance)
            solve    u" + 0.125 u'+ u = 3 cos(0.3t)
                     u(0) = 2; u'(0) = 0
 The red curve is the force f=3cos(0.3t)
 
 

Example 6

Example 6: Forced vibration with damping (resonance)
            solve    u" + 0.125 u'+ u = 3 cos(t)
                     u(0) = 2; u'(0) = 0
 The red curve is the force f=3cos(t)
 
 

Example 7

Example 7: Forced vibration with damping (No resonance)
            solve    u" + 0.125 u'+ u = 3 cos(2t)
                     u(0) = 2; u'(0) = 0
 The red curve is the force f=3cos(2t)

 

Published with MATLAB® 7.6