what are the characteristics of simple harmonic motion
A simple harmonic motion is a special type of oscillation , in which the particle oscillates on a straight line, the acceleration of the particle is always directed towards a fixed point on the line and its magnitude is proportional to the displacement of the particle from this point.
Let x be the displacement ,A be the amplitude,
x = Asin(wt + Ф)
here the maximum and minimum values of sin(wt +Ф) can be +1 and -1 hence the maximum and minimum values of x can be +A or –A. as a result A gives the amplitude or maximum displacement from mean position.
A particle in SHM repeats its motion after a regular time interval. Suppose the particle is at a position x and its velocity is v at a certain time t. after some time , the position x and its velocity will again be v in same direction. This part of motion is one complete oscillation and the time taken in one complete oscillation is called time period T.
T comes out to be 2π/w.
Frequencyis given as reciprocal of T. hence frequency v = 1/T.
The quantity wt + Ф is called phase. It determines status of the particle in SHM. If a particle’s phase is 0 , then it means that particle is crossing mean position.. if phase is π/2 , then x = A from the above mentioned equation of motion.