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The natural ...............

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Solution :Let mass 'm' falls down by x so spring extends by 4x, which causes an extra tension T in lowest string

Thus the MAGNITUDE of T can be found as FOLLOWS :
`implies T/4=K(4x)`
`T=(16k)x`
Thus equation of motion of mass m is
`T= ma`
`implies a=- (16 k)/m x`
Comparing with `a=-omega^(2) x`
we get `omega=sqrt((16 k)/m)`
`implies f=omega/(2pi)=1/(2pi) sqrt((16 k)/m)`
`=2/pi sqrt(k/m)`


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