A small block of mass $2 \mathrm{kg}$ is placed on a bigger block of mass $4 \mathrm{kg}$ which is attached to horizontal spring of spring constant $K=500 \mathrm{N} {\mathrm{m}}^{-1}$ as shown in figure, coefficient of friction between blocks is$0.2$. Maximum amplitude of system so that there is no relative slipping between blocks 

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to massless spring of spring constant $K$. A mass $M$ hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are $A$ and $Y$ respectively. If the mass is slightly pulled down and released, it will oscillate with a time period $T$ equal to

A pendulum has period$T$ for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings in the left of its resting position as shown in the figure. The pendulum is released from rest at a certain point $A$. The time taken by it to return to that point is