Periodic motion, motion repeated in equal intervals of time. 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 around the Sun, and a water wave.
Periodic Motion Graph
Periodic Motion Graph is as shown:
Mathematical Condition of Simple Harmonic Motion
When the restoring force of any motion has equation of form: F=−kx Then fundamentally this equation represents simple harmonic motion.
how to identify periodic and non periodic motion
A motion that repeats itself at regular intervals of time is called periodic motion. Example : Explain whether Functions 1. sinωt+cosωt and 2. e−ωt are periodic or not? 1. we can write sinωt+cosωt as 2sin(ωt+4π) = 2sin(ωt+4π+2π) = 2sin[ω(t+ω2π)+4π] The periodic time of function is ω2π So it is periodic motion. 2. The function e−ωt decreases monotonically with increasing time and tends to zero as t approaches infinity and thus never repeats its value. Hence it is non periodic motion.