Free Forced And Damped Oscillations

To understand free forced oscillation and damped oscillation, you should first have a brief idea about oscillation in general. Oscillation is a measure of some repetitive variation, as a function of time. It can be measured with respect to a state of equilibrium. If the oscillation is mechanical in nature it is referred to as vibration (but sometimes used as a synonym for vibration). The most common and simplest example for oscillation is the motion of a simple pendulum.


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 oscillations. Since these are mechanical in nature, they are also called vibrations. The motion of alternating current (although electrical) is also an example of an oscillatory motion.

If a mechanical motion is such that, the restoring force acts in the direction opposite to that of displacement of the object and is proportional to it, is called a simple harmonic motion. 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.

There are three main types of Simple Harmonic Motion

  • Free Oscillation
  • Forced Oscillation
  • Damped Oscillations

Free Oscillations

These have a constant amplitude and constant period and the main factor is that they are not under any external influences. For the amplitude to remain constant, the system has no damping. But this is possible only in theory as damping will always occur.

Damping is the reduction in amplitude (energy loss from the system) due to overcomings of external forces like friction or air resistance and other resistive forces.

In such a system, the amplitude, frequency, and energy all remain constant.

Forced Oscillations

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.

Damped Oscillations

Oscillation, where the amplitude of a body keeps reducing with time is called a damped oscillation. Along with the decrease in amplitude, the energy of the system also keeps decreasing. There are two types of damping

  • Natural Damping
  • Artificial Damping

Check NCERT solutions to learn more about Oscillations

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.