PERIODIC MOTION

in physics, motion repeated in equal intervals of time, the time of each interval being called the period. Periodic motion is performed, for example, by a rocking chair, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit about the Sun, and a water wave. In each case the interval of time for a repetition, or cycle, of the motion is called a period. In simple harmonic motion (see simple harmonic motion), the period is the time required to complete one vibration. One period therefore equals the reciprocal of the frequency, or 1/frequency; e.g., a hummingbird's wing that beats with a frequency of 50 per second has a period of 0.02 second. When a point moves around a circle with uniform speed, its projection on any line taken as the diameter (i.e., the intersection of a line drawn through the point perpendicular to the diameter) will execute simple harmonic motion. Although the point is moving with constant speed, the projection point will accelerate or decelerate according to whether it is moving toward the centre of the circle or away from it. If the ratio of its displacement distance from the centre to the acceleration is denoted by c, then the period T of a simple harmonic motion is equal to 2p times the square root of c-i.e., T = 2p. Waves that can be represented by harmonic waves-i.e., sine curves-are periodic. If the wave is propagated with a velocity v and has a wavelength l, then the period (T) is equal to wavelength divided by velocity, or T = l/v. Because frequency ( f) is the reciprocal of the period-i.e., f = 1/T-this equation may be written f= v/l.