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

Options

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

Answer

D

Explanation

Here, `m_(2)=2m_(1),` In case of vibrations of a loaded spring, the angular frequency,
`omega=sqrt(k//m)`
`:. (omega_(1))/(omega_(2))=sqrt((k_(1))/(k_(2))xx(m_(2))/(m_(1)))=sqrt((k_(1))/(k_(2))xx2)`
For equal maximum velocity, `A_(1)omega_(1)=A_(2)omega_(2)`
`:. (A_(1))/(A_(2))=(omega_(2))/(omega_(1))=sqrt((k_(2))/(2k_(1)))`