Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.

Options

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

Answer

B

Explanation

`v_("max 1") = v_("max 2")`
`rArr omega_(1) A_(1) = omega_(2) A_(2)`
`rArr sqrt((k_(1))/(m)) A_(1) = sqrt((k_(2))/(m)) A_(2)`
`rArr (A_(1))/(A_(2)) = sqrt((k_(2))/(k_(1)))`
Hence (B) is correct