Q.Distinguish between free vibrations and forced vibrations (Two points).

An object left to oscillate entirely on its own vibrates at its own NATURAL frequency (e.g. a simple pendulum of length l oscillates only at n = (1/2*pi)*sqrt(g/l) if simply displaced and released) -- this is called a free oscillation. If instead a periodic external force drives the object at some other frequency, the resulting motion is a FORCED oscillation, occurring at that external driver's (forced) frequency rather than the object's own natural frequency.

If the forced (driving) frequency happens to exactly EQUAL the object's own natural frequency, the object absorbs the maximum possible energy from the driving source and oscillates with the maximum possible amplitude -- this special, high-response condition is called RESONANCE. A classic demonstration uses several pendula of different lengths hung from a common string, along with a "source" pendulum: when the source is set oscillating, all the others are driven (forced) at its frequency, but only the one sharing its EXACT length (hence its exact natural frequency) swings with a dramatically larger amplitude than the rest -- it is "in resonance" with the source. Plotting (amplitude)^2 ag …