Behaviour of Undamped System:

Let the system illustrated in Figure 2(i). The system is disturbed through pulling the mass by distance 'X'. The answer of the system in this case is specified by equation (11) that is

                 x = X cos w_n t

  ∴        x' =- X w sin w_n t = X w_n cos ( w_n  t + π/2 )

and

These expression mentions that velocity vector leads displacement by π/2 and acceleration leads displacement by 'π' and maximum velocity is (X w_n) and maximum acceleration is

         Figure 5

  Figure 6

Figure 6 indicates the plots of displacement, velocity and acceleration, w. r. t.  time. The following observations may be made from these plots :

 (i) A body if disturbed shall never end vibrating.

 (ii) While displacement is maximum, velocity is zero and acceleration is maximum in direction opposite to displacement.

 (iii) While displacement is zero acceleration is zero and velocity is maximum.