Periodic And Oscillatory Motions - Practice Questions & MCQ

Periodic motion:- A motion, which repeats itself over and over again after a regular interval of time is called a periodic motion.

• The fixed interval of time after which the motion is repeated is called time period of the motion.

• If a particle moves along x -axis, its position depends upon time t. We express this fact mathematically by writing
  x=f(t) or x(t)
  There are certain motions that are repeated at equal intervals of time. By this we mean that particle is found at the same position moving in the same direction with the same velocity and acceleration, after each period of time. Let T be the interval of time in which motion is repeated. Then
  x(t)=x(t+T)
  where T is the minimum change in time. And the function that repeats itself is known as a periodic function. 

• Examples : 

1. Revolution of earth around the sun (period one year)

2. Rotation of earth about its polar axis (period one day)

3. Motion of hour’s hand of a clock (period 12-hour)

Fig:- Examples of Periodic motion

Oscillatory Motion:- Oscillatory motion is that motion in which a body moves to and fro or back and forth repeatedly about a fixed point in a definite interval of time.

• Every oscillatory motion is periodic if energy is not lost anywhere, but every periodic motion need not be oscillatory. Circular motion is a periodic motion, but it is not oscillatory.

• General equation of Oscillatory motion:-

When a body is given small displacement from the equilibrium position, a force starts acting towards the equilibrium position (or mean position) which tries to bring the body back to it’s mean position. And that force is given by:-

$F=-k x^n$, where x is measured from mean position and  n=1,3,5,7,9 etc

1. When x=positive, F=negative

2. When x=negative, F=positive

3. When x=0, F=0,i.e., at mean position