b
(b) When two blocks performs simple harmonic motion together then at the extreme position ( at amplitude \(=A\))

Restoring force \(F = KA = 2ma\)\(⇒\) \(a = \frac{{KA}}{{2m}}\)

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

\(\therefore \) Maximum friction \( = \frac{{KA}}{2}\)