Two springs of constants `k_1` and `k_2` have equal maximum velocities, when executing simple harmonic motion. The ratio of their amplitudes (masses are equal) will be

Options

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

Answer

D

Explanation

`v_(1)=v_(2)`
`A_(1)omega_(1)=A_(2)omega_(2)`
`(A_(1))/(A_(2))=(omega_(2))/(omega_(1))=(T_(1))/(T_(2))=sqrt((k_(2))/(k_(1)))`