(i) In the shown arrangement, both springs are relaxed. The coefficient of friction between `m_(2) " and " m_(1)` is `mu`. There is no friction between `m_(1)` and the horizontal surface. The blocks are displaced slightly and released. They move together without slipping on each other. (a) If the small displacement of blocks is x then find the magnitude of acceleration of `m_(2)`. What is time period of oscillations ? (b) Find the ratio `(m_(1))/(m_(2))` so that the frictional force on `m_(2)` acts in the direction of its displacement from the mean position. (ii) Two small blocks of same mass m are connected to two identical springs as shown in fig. Both springs have stiffness K and they are in their natural length when the blocks are at point O. Both the blocks are pushed so that one of the springs get compressed by a distance a and the other by `a//2`. Both the blocks are released from this position simultaneously. Find the time period of oscillations of the blocks if - (neglect the dimensions of the blocks) (a) Collisions between them are elastic. (b) Collisions between them are perfectly inelastic.

(i) In the shown arrangement, both springs are relaxed. The coefficien

1.	(i) In the shown arrangement, both springs are relaxed. The coefficient of friction between `m_(2) " and " m_(1)` is `mu`. There is no friction between `m_(1)` and the horizontal surface. The blocks are displaced slightly and released. They move together without slipping on each other. (a) If the small displacement of blocks is x then find the magnitude of acceleration of `m_(2)`. What is time period of oscillations ? (b) Find the ratio `(m_(1))/(m_(2))` so that the frictional force on `m_(2)` acts in the direction of its displacement from the mean position. (ii) Two small blocks of same mass m are connected to two identical springs as shown in fig. Both springs have stiffness K and they are in their natural length when the blocks are at point O. Both the blocks are pushed so that one of the springs get compressed by a distance a and the other by `a//2`. Both the blocks are released from this position simultaneously. Find the time period of oscillations of the blocks if - (neglect the dimensions of the blocks) (a) Collisions between them are elastic. (b) Collisions between them are perfectly inelastic.
Answer» Correct Answer - (a) ` a=((k_(1)+k_(2))/(m_(1)+m_(2)))x ; T=2pisqrt((m_(1)+m_(2))/(k_(1)+k_(2)))` (b) `(m_(1))/(m_(2)) gt (k_(1))/(k_(2)); T=2pisqrt((m)/(k))` " for both the blocks in both cases".

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