Oscillation

Oscillation is the repetitive process or variation, typically in a time of some measure. This repetitive variation is about a central value often called a point of equilibrium. The term vibration can also be sometimes used more narrowly to mean a mechanical oscillation but most of the time it is used to be synonymous with oscillation. Examples of oscillation are swinging pendulum, alternating current, etc.

Difference Between Periodic, Oscillatory and Simple Harmonic Motion

A phenomenon, a process in which the motion repeats itself after the equal intervals of time, is called the periodic motion while if the body moves to and fro repeatedly about a mean or equilibrium position it is called oscillatory motion.

All oscillatory motion is periodic but all periodic is not oscillatory and here are examples which are periodic but not oscillatory e.g. bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, etc.

Now let us understand simple harmonic motion let us understand with help of example. If  we rotate the disk from its rest position i.e where the reference line is at 0 and release it, it will oscillate about that position in angular simple harmonic motion and x varies  in time according to the relationship:

x(t)=xmcos(wt+f)

in which x,w,f are constants of the motion. By differentiating x(t) with respect to time twice, we obtain an equation for the angular acceleration of the disk.

a(t)=−w2x(t)

Types of Oscillatory Motion

Damped Oscillation

Damping the process of restraining and controlling the oscillatory motion, such as mechanical vibrations, by dissipating some amount of energy as required. The process of oscillation remains undamped when a restoring force equal to the restraining force is induced and hence the system oscillates with the same energy. Now when the restoring force is not applied the oscillation process suddenly stops and when the restoring force acting is less than​ the restraining force, damping is introduced. Therefore, Damped oscillations are classified according to the difference in energy between restoring force applied and the restraining force acting. A damped oscillation is an oscillation that fades away with respect to time i.e it reduces in magnitude with time.

Damped oscillations are mainly be classified into three major types

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a) Under damped oscillations: Damping constant <1

b) Critically damped oscillations: Damping constant = 1

c) Over damped oscillations: Damping constant >1

a) Under damped Oscillation: In underdamped oscillation reaches the equilibrium position or point faster but oscillations occur mainly across the equilibrium point one or more time. The oscillation becomes stable and slow. Under damped oscillations, it has the least energy dissipation compared to other damping systems.

b) Critically damped Oscillation: In case of Critically damped oscillation damping of the oscillation causes it to return to its equilibrium position fast and does not create any oscillations back and forth about that same point. Critical damping is the damping in which the damping constant equals to one. Critical damping is the most precise damping required for the system. In this oscillation, the damping is applied in such a way that the force available is just sufficient to bring the oscillation into equilibrium without any further back and forth movement (oscillations).

c) Over damped Oscillation: Over damped Oscillation: In this oscillation reach equilibrium position slowly and does not have any oscillations across the equilibrium point is termed as overdamped oscillations. In overdamped oscillations, the damping constant value is greater than one. The energy dissipation is higher in this case as compared with other damping systems.

Simple Harmonic Motion as Oscillation

Simple harmonic motion can be classified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law.  Here also repeated back and forth movement over the same path about an equilibrium position, such as a mass on a spring or pendulum is taking place. In other words, SHM is an oscillatory motion where the net force on the system is restoring in nature.

One of the specialties of SHM is that restoring force is proportional to the displacement from equilibrium and both the magnitude of the restoring force and the acceleration are the greatest at the maximum points of displacement of the body. The negative sign informs us that the force and acceleration are there in the opposite direction from displacement.