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. `(mum_(2)g(m_(1)+m_(2)))/(m_(1)k_(2)-m_(2)k_(1))`
B. `(mum_(1)g(m_(1)+m_(2)))/(m_(2)k_(1)-m_(1)k_(2))`
C. `(mu m_(1)g(m_(1)+m_(2)))/(m_(1)k_(1)-m_(2)k_(2))`
D. `(mu m_(2)g(m_(1)+m_(2)))/(m_(1)k_(1) -m_(2)k_(2))`

Answer

A

Explanation

`f = k_(2)A - m_(2) omega^(2)A le mu m_(2)g`
`rArr A le (mu m_(2)g)/(k_(2)-m_(2) omega^(2))` and `omega = sqrt(((k_(1)+k_(2))/(m_(1)+m_(2))))`