Change in amplitude of pendulum

[Pathan]

When we drag the bob at certen heightand relese it. It start's oscelation. and the the apmlitude of the vibration decreases with time.
can anybody help me by giving the equation which tell the decrease in amplitude.

 

[CompuChip]

No, because in general it won't because we assume an ideal pendulum.
If the amplitude decreases there are energy losses which may be due to a variety of factors, most importantly (but not limited to) air friction and possibly friction at the pivot. Unless you make some more assumptions you cannot just write down "the" equation (and even under some set of assumptions, "the" equation will usually be a differential equation which is hard to solve).

 

[Bob S]

The amplitude loss is probably due to air drag. There are two types, corresponding to low and high Reynold's numbers. Read http://en.wikipedia.org/wiki/Drag_(physics )
Your pendulum should have a high density bob (lead is better than brass), and as long a string as possible. Note that for a given density bob, the mass is proportional to the cube of linear dimensions, and the frontal area (proportional to drag) scales as the square.