Ratio of force constants of two springs is 1 : 2 and the ratio of mechanical energy of them is 2 : 9, ratio of amplitudes of two bodies suspended at the end of spring is……….

Explanation

`(E_1)/(E_2)= ((1)/(2)k_(1)A_(1)^(2))/((1)/(2)k_(2)A_(2)^(2))`
`therefore (2)/(9)= (1)/(2)xx ((A_1)/(A_2))^(2)`
`therefore (2)/(9)xx (2)/(1) = ((A_1)/(A_2))^(2)`
`therefore (4)/(9)= ((A_1)/(A_2))^(2)`
`therefore (A_1)/(A_2)= (2)/(3)`.