about the origin of an x -axis between the limits + A and – A as shown in Fig. . . This oscillatory motion is said to be simple harmonic if the displacement x of the particle from the origin varies with time as : x ( t ) = A cos ( ω t + φ ) ( .
) Fig. . A particle vibrating back and forth about the origin of x-axis, between the limits +A and –A. where A , ω and φ are constants.
Thus, simple harmonic motion (SHM) is not any periodic motion but one in which displacement is a sinusoidal function of time. Fig. . shows the positions of a particle executing SHM at discrete value of time, each interval of time being T / , where T is the period of motion.
Fig. . plots the graph of x versus t , which gives the values of displacement as a continuous function of time. The quantities A , ω and φ which characterize a given SHM have standard names, as summarised in Fig.
. . Let us understand these quantities. The amplitutde A of SHM is the magnitude of maximum displacement of the particle.
[Note, A can be taken to be positive without any loss of generality]. As the cosine function of time varies from + to – , the displacement varies between the extremes A and – A . Two simple harmonic motions may have same ω and φ but different amplitudes A and B , as shown in Fig. .
(a). While the amplitude A is fixed for a given SHM, the state of motion (position and velocity) of the particle at any time t is determined by the Fig. . The location of the particle in SHM at the discrete values t = , T/ , T/ , 3T/ , T, 5T/ .
The time after which motion repeats itself is T. T will remain fixed, no matter what location you choose as the initial (t = ) location. The speed is maximum for zero displacement (at x = ) and zero at the extremes of motion. Fig.