Calculate the maximum extension of the spring in the following two cases. Also calculate period of oscillation in each case.
(a)

Explanation

`ma-ky`
`"so that "a=(-ky)/(m)" and "(y)/(a)=|-(m)/(k)|`
Hence `T=2pisqrt((y)/(a))` may be written as`" "T=2pi sqrt((m)/(k))`
Maximum extension of the spring will be .y.
(b) `ma=-2ky`

`"so that "(y)/(a)=|-(m)/(2k)|" "{:("Altermaively"),(mua=-ky),("where "mu=(m_(1)m_(2))/(m_(1)+m_(2))=(m)/(2)):}`
`&T=2pisqrt((y)/(a))" "{:(therefore (ma)/(2)=-ky),("or ma "=-2ky):}`
`T=2pisqrt((m)/(2k))" "ma=-k(2y)`
Maximum extension of the spring will be .2y..