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A body of mass m is attached to one end ...

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand, so that the spring is neighter stretched nor comprssed. Suddenly the support of the hand is removed. The lawest position attained by the mass during oscillation is 4 cm below the point, where it was held in hand.

Text Solution

Verified by Experts

The periodic time of oscillation of body suspended at the end of spring is `T= 2pi sqrt((m)/(k))`, does not depend on the amplitude and frequency
`v= (1)/(2pi) sqrt((k)/(m))`
but from equation (2)
`(k)/(m)= (g)/(x.)`
`= (9.8)/(2xx 10^(-2))= 490`
`therefore v= (1)/(2pi) sqrt((k)/(m))`
`=(1)/(2xx 3.14) sqrt(490)`
`=(1)/(6.28)xx 22.1`
`=3.519 Hz`
`approx 3.52 Hz`.
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