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

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(B) When two blocks perform simple harmonic motion together,the system acts as a single body of mass $2m$ attached to a spring of constant $k$.The acc

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$\frac{kA}{2}$

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(B) When two blocks perform simple harmonic motion together,the system acts as a single body of mass $2m$ attached to a spring of constant $k$.The acceleration of the system at any displacement $x$ is given by $a = -\omega^2 x$,where $\omega^2 = \frac{k}{2m}$.At the extreme position,the displacement is $x = A$,so the magnitude of acceleration is $a_{max} = \omega^2 A = \frac{k}{2m} A = \frac{kA}{2m}$.The friction force $f$ acting on block $P$ provides the necessary acceleration to it. Since block $P$ has mass $m$,the friction force is $f = m \cdot a$.At the extreme position,the friction force reaches its maximum value: $f_{max} = m \cdot a_{max} = m \left( \frac{kA}{2m} \right) = \frac{kA}{2}$.

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