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_(1)/(k_(2)))^(1//2)`
C. `(k_(2))/(k_(1))`
D. `(k_(2)/(k_(1)))^(1//2)`

Answer

B

Explanation

Since maximum velocity is `Aomega` where `omega` is angular frequency,
`therefore A_(1)omega_(1)=A_(2)omega_(2)or(A_(1))/(A_(2))=(omega_(2))/(omega_(1))`
But `omega=sqrt((k)/(m))therefore (A_(1))/(A_(2))=sqrt(k_(2))/(sqrt(k_(1)))=sqrt((k_(2))/(k_(1)))`