If a particle moves such that it repeats its path regularly after equal intervals of time , it's motion is said to be periodic.
The interval of time required to complete one cycle of motion is called time period of motion.
If a body in periodic motion moves back and forth over the same path then the motion is said to be viberatory or oscillatory.
Examples of such motion are to and fro motion of pendulum , viberations of a tuning fork , mass attached to a spring and many more.
Every oscillatory motion is periodic but every periodic motion is not oscillatory for example motion of earth around the sun is periodic but not oscillatory.
Simple Harmonic Motion (or SHM) is the simplest form of oscillatory motion.
SHM arises when force on oscillating body is directly proportional to the displacement from it's equilibrium position and at any point of motion , this force is directed towards the equilibrium position.
2. Simple Harmonic Motion (or SHM)
SHM is a particular type of motion very common in nature.
In SHM force acting on the particle is always directed towards a fixed point known as equilibrium position and the magnitude of force is directly proportional to the displacement of particle from the equilibrium position and is given by
where k is the force constant and negative sign shows that fforce opposes increase in x.
This force os known as restoring force which takes the particle back towards the equilibrium position , and opposes increase in displacement.
S.I. unit of force constant k is N/m and magnitude of k depends on elastic properties of system under consideration.
For understanding the nature of SHM consider a block of mass m whose one end is attached to a spring and another end is held stationary and this block is placed on a smooth horizontal surface shown below in the fig.
Motion of the body can be described with coordinate x taking x=0 i.e. origin as the equilibrium positionwhere the spring is neither stretched or compressed.
We now take the block from it's equilibrium position to a point P by stretching the spring by a distance OP=A and will then release it.
After we release the block at point P, the restoring force acts on the block towards equilibrium position O and the block is then accelerated from point P towards point O as shown below in the fig.
Now at equilibrium position this restoring force would become zero but the velocity of block increases as it reaches from point P to O.
When the block reaches point O it's velocity would be maximum and it then starts to move towards left of equilibrium position O.
Now this time while going to the left of equilibrium position spring is compressed and the block moves to the point Q where it's velocity becomes zero.
The compressed spring now pushes the block towards the right of equilibrium position where it's velocity increases upto point O and decreases to zero when it reaches point P.
This way the block oscillates to and fro on the frictionless surface between points P and Q.
If the distance travelled on both sides of equilibrium position are equal i.e. , OP=OQ then the maximum displacement on either sides of equilibrium are called the Amplitude of oscillations.