Periodic motion

Periodic motion

Everything that happens in our daily life follows a peculiar rhythm and pattern. Starting from the way we walk to the grinding of a mixer, flowing of water, everything follows a unique pattern. Even the earth’s rotation around the sun is an example of this rhythmicity.

Haven’t you noticed a rocking chair or a bouncing ball? Don’t you think these events also follow a pattern or a rhythm? Yes! They do. These motions are called periodic motions. Periodic motion is a motion that occurs repeatedly at regular intervals of time.

Properties of periodic motion

The objects that are in periodic motion have three characteristics:

• Velocity
• Period
• Amplitude

A special type of periodic motion is known as simple harmonic motion.

Oscillation

A classic example of oscillatory motion is the pendulum’s motion. The back and forth movement of the pendulum follows a rhythmic pattern, and it repeats itself at regular intervals of time.

Oscillation can be defined as the to and fro motion of a body about a fixed position.

Every oscillatory motion is a periodic motion. However, every periodic motion is not oscillatory.

Vibrations- The increase in the frequency of oscillations leads to vibrations.

E.g., Vibrations of the string in string instruments.

Other examples of oscillatory motion are the movement of tides in the sea, the vibrations of string instruments, the movement of spring.

Oscillations can be further divided into three

• Damped oscillations
• Undamped oscillations
• Forced oscillations

Damped oscillation

We have seen the motion of a pendulum that continues for a long time, but eventually, its motion dies out. This happens because the air drags, and friction opposes the pendulum’s movement and dissipates its energy. Here, the pendulum is said to have executed damped oscillation.

The process of controlling the oscillatory motion by dissipating energy is called damping.

It does not occur voluntarily; it happens when the restoring force that brings the body to its equilibrium position is less than the restraining force.

Damped oscillations are classified into three based on the difference in the energy between restoring and restraining force.

• Under damped oscillations
• Critically damped oscillations
• Over damped oscillations

We can see countless examples of damped oscillations in our daily life.

• The movement of the swing fades away when no pumping force is applied.
• Shock absorbers in vehicles reduce the vibrations caused by a vehicle.

Undamped oscillations

Undamped oscillations comprise the ideal oscillations that are not affected by any external factors and hence never stop. However, this is not observed in real life, where various external factors can restrict periodic motion.

Forced Oscillations

Forced oscillations are acted upon by an external force and hence can counter the dissipative forces that exist in our environment.  This is observed in an AC Circuit where the external force is provided by the power supplier and the dissipative forces are losses in the form of heat and usage in appliances.

Considering the wave motion, let’s see some parameters related to periodic motion.

Period- Period is the time taken by the motion to repeat itself. The SI unit of period is seconds.

Frequency- The number of times a motion is repeated in one second. The unit of frequency is Hertz (Hz).

The periodic motion formula can be given by

f = 1/T

This is the relation between frequency and time in periodic motion.

Simple harmonic motion

Simple harmonic motion can be defined as an oscillatory motion that occurs in a straight line between two extreme points. A restoring force mainly acts on the body in simple harmonic motion and is directly proportional to the displacement from its equilibrium position. The equilibrium position is the point where the body experiences no force.

Consider a simple pendulum oscillating back and forth about an axis between two extreme limits.

The pendulum is considered to be in simple harmonic motion.

The particle moves in a to and fro motion directly from the point -A to +A. This motion is said to be in simple harmonic motion only if the displacement of the particle, say ‘X’ from the equilibrium position, changes with time’ t.’

And it is given by the formula,

x(t) = A cos (ωt + Φ)

Where x(t) – is the displacement of the particle as a function of time

A – Amplitude (Maximum displacement of a particle from its mean position)

ω = angular frequency

Φ = phase constant

ω t + Φ = Phase angle.

Simple harmonic motion is a periodic motion in which displacement is a sinusoidal function of time.

What is non-periodic motion?

A motion that repeats itself but not in regular intervals of time is called non-periodic motion.

• Swinging of the branches of the tree
• Movements of the batsmen running between the wickets

Applications of periodic motion

• The pendulum of a clock
• Children jumping on a trampoline
• Rotation of the earth around the sun

Conclusion

As mentioned earlier, everything on earth follows a pattern if you carefully observe. Even the rotation of the earth itself is a periodic motion. Just imagine if the earth stops rotating around the sun? As you all know, the periodic rotation of the earth brings about day and night, and it marks the very existence of life on earth. Just imagine a day when this fails to happen? We all are doomed. Such is the importance of periodic motion in our life. So periodic motion is not just a motion; it is a rhythm in our lives too.