Hello dear students we know that there are two types of oscillations, viz: free oscillations and forced oscillations. When the object is oscillating due to its natural frequency, is said to have free oscillations. Whereas when oscillations of particles are due to external periodic forces, then the oscillations as known as forced oscillations.
If any particle is performing oscillations with constant amplitude throughout, then the oscillations are known as undamped oscillations. When the motion of an oscillator is reduced by an external force, the oscillator and its motion are said to be damped.
Let’s define and learn the concept of damped oscillations in detail……..!
Definition:
Periodic oscillations of gradually decreasing amplitude are called damped harmonic oscillations and the oscillator is called damped harmonic oscillator.
An idealized example of damped oscillator is shown in figure below.
Block of mass ‘m’ oscillates vertically on a spring with spring constant k. From the block, a rod extends to Vane that is submerged in liquid experiences damping force. The damping force depends upon nature of surrounding medium.
The damping force Fd is directly proportional to velocity ‘v’ of vane and block.
Fd α v i.e. Fd =-b v
Where ‘b’ is damping constant and negative sign indicates that Fd opposes the motion.
The force on the block from spring is, Fs =-k x. Let us assume that the gravitational force on the block is negligible compared to Fd& Fs. Thus the total force acting on the block at any time ‘t’ is,
The above is the differential equation for damped harmonic oscillations.
The amplitude decreases with time exponentially as shown in displacement-time graph shown below.