A block suspended from a vertical spring is in equilibrium. Show that the extension of the spring equals the length of an equivalent simple pendulum, i.e., a pendulum having frequency same as that of the block.

Answer

A

Explanation

Time period of simple pendulum
`=2pi(sqrtl/g))`
Time period of spring in `2pisqrt(m/k)`
`T_P=T_S=[Frequency is mall]`

`(sqrt(l/g))=(sqrt(m/k))`
`rarr (l/g)=(m/k)`
`rarr l=mg/k=F/k=x`
because restoring force =weight `=F=mg`
`rarr l=x`(proved)