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A block of mass \( M \) slides on a frictionless surface with an initial speed of \( v_{0} \). On top of block is a small box of mass \( m \). The coefficients of friction between box and block are \( \mu_{s} \) and \( \mu_{k} \). The sliding block encounters an ideal spring with force constant \( k \). Answer following questions.
Assuming no relative motion between box and block what is the maximum possible acceleration of block and box at the instant of maximum compression?
(1) \( \mu g \)
(2) \( \frac{\mu_{s} M g}{m} \)
(3) \( \frac{\mu_{s}(M+m) g}{m} \)
(4) \( \frac{\mu_{s} m g}{M} \)
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