A weight is suspended from a spring balance and the time period for its vertical oscillatory motion is T. The spring is divided into two equal parts and from any one of them the same weight is suspended. Determine the time period of vertical oscillatory motion of that spring.

A weight is suspended from a spring balance and the time period for it

1.	A weight is suspended from a spring balance and the time period for its vertical oscillatory motion is T. The spring is divided into two equal parts and from any one of them the same weight is suspended. Determine the time period of vertical oscillatory motion of that spring.
Answer» Solution :If the INCREASE in length of the spring is l due to the suspension of the weight, then spring constant, `k=(mg)/l`, i.e., if the weight remains constant, then `kprop1/l`. Now, if the spring is halved and the same weight is suspended, then increase in length is ALSO halved. So the spring constant (k) is doubled. Now, time period, `T=2pisqrt(m/k)or,Tprop1/sqrtk` So, as k is doubled, time period becomes `1/sqrt2` TIMES the original time period, i.e,. the required time period = `T/sqrt2`.