Free Forced And Damped Oscillations

In Physics, Oscillation is a repetitive variation, typically in time. Measured between two or more different states or about equilibrium or about a central value. Some familiar examples for oscillations in clues Alternating Current, Simple pendulum. Some parameter governing oscillation is Period of oscillation, Oscillation frequency, Oscillation amplitude.

What Is Oscillation?

In general, An oscillation is a back and forth movement in a regular rhythm. In physical interpretation Oscillation definition is defined as the regular variation in position or magnitude about a central point or about a mean position. Typically measured using the unit of an oscillation frequency that is in terms of the unit of frequency: Hertz

Free Forced and Damped Oscillations

Schematic representation of a damped oscillation.

Oscillations Physics

Oscillations in physics are quantified using the parameters like – Frequency, Amplitude and period. Each term are explained as follows-





Period Of Oscillation

Time for one complete oscillation is called Period.



Oscillation Frequency

The number of cycles/oscillations per second is called the frequency of oscillation.



Oscillation amplitude

Maximum displacement from the mean position is called the amplitude of oscillation.



Oscillation Formula

The formula for parameters governing oscillations in Physics are listed below-

  • Period of oscillation:Time period of simple pendulum can be mathematically expressed as
    \(T=2\pi \sqrt{\frac{L}{g}}\)
    T is the Time Period of oscillation
    L is the length
    g is the acceleration due to gravity
  • Oscillation frequency: Mathematically expressed as –
    T is the Time period of oscillation.

Oscillation Examples

Did you know that the vibration of a guitar string is an example of oscillations? The motions of a playground swing, tuning forks are also examples of oscillatory motion. Since these are mechanical in nature, they are also called vibrations. The motion of alternating current (although electrical) is also an example of oscillatory motion.

Simple Harmonic Motion

It is the simplest form of oscillatory motion which all of us come across in our day today life. It is an oscillatory motion in which retarding force proportional to the amount of displacement of an object from an equilibrium position. Or in other words, the restoring force acts in the direction opposite to that of displacement of the object and is proportional to it.

Again, the motion of a simple pendulum is a perfect example for this, where if it is displaced to one direction, the restoring force acts in the opposite direction. Any simple harmonic motion can be categorised into three types of oscillation.

Types Of Oscillation

There are three main types of Simple Harmonic Motion

  • Damped Oscillation
  • Forced Oscillation
  • Free Oscillation

Free Oscillation

The Free oscillation posses constant amplitude and period without any external force to set the oscillation. Ideally, free oscillation does not undergo damping. But in all natural systems damping is observed unless and until and unless any constant external force is supplied to overcome damping. In such a system, the amplitude, frequency, and energy all remain constant.

Damped Oscillation

The damping is a resistance offered to the oscillation. The oscillation that fades with time is called damped oscillation. Due to damping, the amplitude of oscillation reduces with time. Reduction in amplitude is a result of energy loss from the system in overcomings of external forces like friction or air resistance and other resistive forces. Thus, with the decrease in amplitude, the energy of the system also keeps decreasing. There are two types of damping

  • Natural Damping
  • Artificial Damping

Forced Oscillation

When a body oscillates by being influenced by an external periodic force, it is called forced oscillation. Here, the amplitude of oscillation, experiences damping but remains constant due to the external energy supplied to the system.

For example, when you push someone on a swing, you have to keep periodically pushing them so that the swing doesn’t reduce.

Practice Questions For Oscillation

Q 1) Can a motion be oscillatory but not simple harmonic? Explain with valid reason.

Ans: Yes.
Consider an example of the ball is dropping from a height on a perfectly elastic surface, the type of motion involved here is oscillatory but not simple harmonic as restoring force F=mg is constant and not F∝−x, which is a necessary condition for simple harmonic motion.

Q 2) What is the basic condition for the motion of a particle to be simple harmonic motion?

Ans: The restoring force acting on it is proportional to its displacement from the mean position. That is, F=−kx.

Q 3) What happens to the oscillation of the body in damped oscillation?

Ans: The oscillation of the body decreases with time.

Q 4) What is free oscillation?

Ans: Free oscillation is the oscillation of the particle with a fundamental frequency under the influence of restoring force.

Q 5) In free oscillation, what happens to the amplitude, frequency and energy of the oscillating body?

Ans: In free oscillation, the amplitude, frequency and energy of the oscillating body remain constant/unchanged.

Q 6) Why the frequency of free oscillation is called natural frequency?

Ans: Frequency of free oscillation depends on the nature and the structure of the oscillating body.

Q 7) Name a few damping forces

Ans: Some of the damping forces are – Hysteresis force, viscous force and frictional force.

Q 8) In damping oscillation, Why does the oscillation decrease exponentially?

Ans: In damping oscillation decrease in the energy results in a decrease in amplitude of oscillation.

Q 9) What is damping force?

Ans: Force produces a resistance to the oscillation.

Q 10) What is forced oscillation?

Ans: When oscillation of a body is under the influence of external force the oscillation is called forced oscillation.

Q 11) How does the damping effects amplitude in forced oscillation?

Ans: The forced oscillation does face the damping effect. But the supply of external force results in gaining the energy thereby maintaining constant amplitude.

Q 12) What is resonance?

Ans: Oscillation of object with maximum amplitude, when the frequency of the applied force equal to the natural frequency of the object is called resonance.

Q 13) When resonance can be observed?

Ans: When the frequency of the applied force equal to the natural frequency of the object.

Q 14) What is the nature of the frequency in forced oscillation?

Ans: In forced oscillation, the frequency of the damped oscillation is equal to the frequency of the applied external force.

Q 15) Can a motion be periodic and not oscillatory?

Ans: Yes.
In the case of uniform circular motion; It is periodic but not oscillatory.

Hope you have understood about Oscillation, What is oscillation, Oscillation definition, Types of oscillation, oscillation Examples, Simple Harmonic motion and its types like – Free oscillation, damped oscillation and forced oscillation along with formula, terms, symbol and SI units.

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Practise This Question

For the damped oscillator shown, the mass m of the block is 200 g, k = 90 N m1 and the damping constant b is 40 g s1. What is the period of oscillation, time taken for its amplitude of vibrations to drop to half of its initial value.