A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. µ s is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is
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When two blocks perform simple harmonic motion together then at the extreme position (at amplitude = A ) Restoring force $F = KA = 2 m a \Rightarrow a = \frac{KA}{2 m}$
There will be no relative motion between P and Q if pseudo force on block P is less than or just equal to limiting friction between P and Q.
i.e. $m\left(\frac{KA}{2m}\right)=$ Limiting friction
$\begin{matrix} \bullet \\ \bullet & \bullet \end{matrix}$ Maximum friction $= \frac{\mathrm{KA}}{2}$
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