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The arrangement shown in
figure is at rest. An ideal spring
of natural length \( l_{0} \) having
spring constant \( k=220 \mathrm{Nm}^{-1} \), is
connected to block \( A \). Blocks \( A \)
and \( B \) are connected by an ideal
string passing through a friction less pulley. The mass of
each block \( A \) and \( B \) is equal to \( m=2 \mathrm{~kg} \) when the spring was
in natural length, the whole system is given an acceleration
\( \vec{a} \) as shown. If coefficient of friction of both surfaces is
\( \mu=0.25 \), then find the maximum extension (in \( \mathrm{cm}) \) of the
spring. \( \left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right) \).
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