A block P of mass m is placed on a smooth hor | vedclass

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(C) The system consists of two blocks of mass $m$ each,moving together as a single unit. The total mass of the system is $M = m + m = 2m$.The angular

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$\frac{KA}{2}$

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(C) The system consists of two blocks of mass $m$ each,moving together as a single unit. The total mass of the system is $M = m + m = 2m$.The angular frequency of the oscillation is given by $\omega = \sqrt{\frac{K}{M}} = \sqrt{\frac{K}{2m}}$.The maximum acceleration of the system is $a_{max} = \omega^2 A = \left(\frac{K}{2m}\right) A = \frac{KA}{2m}$.The frictional force $f$ provides the necessary acceleration to the lower block $P$. Since block $P$ has mass $m$,the force required to accelerate it is $f = m \cdot a_{max}$.Substituting the value of $a_{max}$,we get $f = m \cdot \left(\frac{KA}{2m}\right) = \frac{KA}{2}$.Thus,the maximum frictional force between the blocks is $\frac{KA}{2}$.

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