The motion of a simple pendulum swinging in air, dies out eventually. This is because the air drag and the friction at the support oppose the motion of the pendulum.
The mechanical energy of the oscillating system opposite to this resistive force is dissipated in the form of heat energy and hence mechanical energy decreases. As a result according to `E= (1)/(2) kA^(2)` the amplitude gradually decreases.
Damped oscillations : ..Oscillations in which the amplitude of the oscillator decreases with time then such type of oscillations is known as damped oscillations...
According to as shown in figure let us consider a block of mass m connected to an elastic spring of spring constant k oscillating vertically.
If the block is pushed down a little and released, it oscillates in vertical plane.
Its angular frequency of oscillation is `omega = sqrt((k)/(m))`.
In practice, the surrounding medium (air) will exert a damping force on the motion of the block and the mechanical energy of the block spring system will decrease.
The energy loss will appear as heat of the surrounding medium (and the block also).
The damping force depends on the nature of the surrounding medium. If a block is immersed in a liquid, the magnitude of damping will be much greater and the disspation of energy much faster.
The damping force is generally proportional to the velocity of the bob.
