Oscillatory Motion and Periodic Motion

Everyone is aware of oscillations and waves. Maybe not scientifically, but simply, we are surrounded by these oscillations and waves. So, how are oscillations different from waves? An oscillation is defined as a disturbance that repeats with time, but a wave is a disturbance that repeats with time and space. This means the wave is periodic in space along with the repetition with time. An example of an oscillation can be a pendulum, going back and forth, whereas sound waves, electromagnetic waves etc., can be an example of waves. Anything that goes to and fro is considered oscillating. But, when these oscillations are combined, they form a wave. Now, let’s go deep and understand the fundamentals of oscillations and waves.

Oscillatory Motion

What is oscillatory motion? The direction in which a pendulum moves is an oscillatory motion. The rocking chair moves back and forth, also an oscillatory motion. The common thing between these two examples is in both cases, the motion is repeated. The time a particle takes to complete one full oscillatory motion is called a period of oscillation. There are certain terms related to oscillatory motion. Let’s understand these terminologies:

• Period: This is the total time needed to move back and forth. This is the time for a single repetition of motion. It is denoted by T.

• Frequency: It is the number of repetitions per unit time. It is represented by f.

• Amplitude: It is the maximum distance travelled by the oscillator. It is denoted by A. In the case of a pendulum, the maximum height it goes to is considered its amplitude.

• Functions: These are the periodic functions denoted by sine and cosine functions of the period and different coefficients. 

One complete motion of an oscillator is called a period. 

Types of oscillations

Oscillations are of three types: Free, damped and forced oscillations.

• Free oscillation: It is when an oscillator oscillates with its frequency. The free oscillation has a constant amplitude and period without giving any external force—for example, a tuning fork.

• Damped oscillations: The oscillation that decreases with time is called damped oscillation. The free oscillations are affected by external factors like friction air resistance, eventually resulting in dying out. These dying free oscillations that continuously decrease with time are damped oscillations. The amplitude and energy of the system will keep decaying with time. 

• Forced oscillations: As the name suggests, any oscillations that are forced to happen with external factors are forced oscillations. Three forces are acting on oscillation systems:

1. Conservation force

2. Damping force

3. Excitation force

In this case, the damping of oscillation rarely happens because of the continued supply of the external forces.

The phenomenon of forcing an oscillation system near its natural frequency is called resonance.

Waves

According to Webster’s dictionary, a wave is defined as:

A variation or disturbance which transfers energy consecutively/progressively from a given point to another point in a medium and may take the form of elastic deformation or a variation of pressure, electric potential, electric or magnetic intensity or temperature.

The definition focuses mainly on the disturbance or variation and the medium through which the wave travels. A medium consists of oscillating particles and these particles are interconnected. The direction in which the wave propagates its energy is called the wave-ray. The wavefront is perpendicular to a wave-ray. The distance between two wavefronts is called a wavelength. The distance between two neighbouring particles of the same oscillating phase is called wave propagation. Wave propagation is independent of location and time.

Types of waves

There are mainly two types of waves- transverse and longitudinal waves. But there are also the waves travelling in 1-D, 2-D and 3-D directions. So, below are the types of waves:

• Transverse waves: The particles oscillate perpendicularly to the wave travelling direction. 

• Longitudinal waves: The particles oscillate to and fro in the direction of propagation. If the particle oscillates in the direction of the wave travelling, then it creates compression. If the particle is oscillating opposite the direction of the wave travelling, then it creates a vacuum (rarefaction). Compressions and rarefactions come in alteration. 

• Plane waves: These are one-dimensional waves travelling in a single direction. 

• Surface waves: Waves that travel in two directions and are two-dimensional waves. 

• Sky Waves: The waves travelling in all three dimensions are Sky Waves.

Waves can travel any distance if the oscillation is smaller at some point. Waves can have different behaviours when they enter a medium or if they are encountered with some obstacles. These behaviours of waves are called reflection, refraction, diffraction or interference. Reflection is the behaviour when a wave hits an obstacle. Refraction is where the wave travels in a medium. During refraction, the speed of the wave depends on the medium properties. While in diffraction, when a wave hits any obstacles, it either spreads out or passes through the obstacle. Interference is where two waves meet and can be constructive or destructive. 

Conclusion

In oscillation, objects move to and fro and the motion is periodic, but the waves behave differently and create reflection, refraction, diffraction and interference. Simple Harmonic Motion (SHM) is the simplest form of motion in which the applied force is directly proportional to the displacement of particles. The key points of oscillations are amplitude and frequency and for waves, the key point is the medium.