In the shown arrangement, both the spring are in their natural lengths. The coefficient of friction between `m_(2)` and `m_(1)` is `mu`. There is no friction between `m_(1)` and the surface. If the blocks are displaced slightly, they together perform simple harmonic motion. Obtain

(a) Frequency of such oscillations.
(b) The condition if the friction force on clock `m_(2)` is to act in the direction of its displacement from mean position.
( c) If the condition obtained in (b) is met, what can be maximum of their oscillations ?

Options

A. `(m_(1))/(k_(1)) lt (m_(2))/(k_(2))`
B. `(m_(1))/(m_(2)) gt(k_(1))/(k_(2))`
C. `m_(1)k_(2) =m_(2)k_(1)`
D. frictional force is never in the direction of displacement

Answer

B

Explanation

Assume blocks are displaced towards right, the free body diagram of `m_(2)` execpt frictional force is:

if frictional force acts towards right, then
`k_(2)x -friction =m_(2)omega^(2)x rArr k_(2)x gt m_(2) omega^(2)x`
`rArr k_(2) gt m_(2) ((k_(1)+k_(2))/(m_(1)+m_(2))) rArr (m_(1))/(m_(2)) gt (k_(1))/(k_(2))`