14 6 Graphical Representation Of S H M – Class 12TH Physics

14.6 Graphical Representation of S.H.M

The graphical representations of displacement, velocity and acceleration of a body executing SHM is given in Fig. 14.9 (a, b and c).

(i) The displacement of the particle executing SHM is given by the expression:

x = x_{o}\cos\omega t \quad \ldots (14.19)

This shows that the particle will have maximum displacement ( $x_{o}$ ) at extreme position.

(Fig. 14.9 (a): Graphical representation of displacement of oscillation performing S.H.M)

(ii) The velocity of the particle executing SHM is given by the expression:

v = x_{o}\omega\sin(\omega t) \quad \ldots (14.20)

The velocity of the particle is maximum (i.e., $v = x_{o}\omega$ ) at the mean position and zero at the extreme positions.

(Fig. 14.9 (b): Graphical representation of velocity of oscillation performing S.H.M)

(iii) The acceleration of the particle executing SHM is given by the expression:

a = -\omega^{2}x

Putting $x = x_{o}\cos\omega t$ , we have:

a = -x_{o}\omega^{2}\cos(\omega t) \quad \ldots (14.21)

The acceleration will be maximum (i.e., $x_{o}\omega^{2}$ ) at the extreme positions, and zero at the mean position.

(Fig. 14.9 (c): Graphical representation of an acceleration of oscillation performing S.H.M)

From the graph of Eqs. (14.19), (14.20) and (14.21) shown in Figs. 14.9 (a, b and c) can be seen that:

However, it must be noted that the phase difference between displacement, velocity and acceleration is $\pi/2$ .