1.

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 ?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» Correct Answer - A
`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))))`


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