Two springs, of spring constants `k_(1)` and `K_(2)`, have equal highest velocities, when executing SHM. Then, the ratio of their amplitudes (given their masses are in the ratio `1:2`) will be

Options

A. `sqrt(k_(1)//k_(2))`
B. `k_(1)//k_(2)`
C. `k_(2)//k_(1)`
D. `sqrt(k_(2)//k_(1))`

Answer

D

Explanation

`(1)/(2)mv^(2) = (1)/(2)K_(1)x_(1)^(2)`
`(1)/(2)mv^(2) = (1)/(2)K_(2)x_(2)^(2)`
`K_(1)x_(1)^(2) = K_(2)x_(2)^(2)`
`(x_(1))/(x_(2)) = sqrt((K_(2))/(K_(1))`