A mechanical system consists of a cubic block of mass (M) and a spring of elastic constant

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A mechanical system consists of a cubic block of mass \(M\) and a spring of elastic constant \(k\) and negligible mass rigidly anchored above the block. The cube \(M\) is stationary on a horizontal plane with friction, and the coefficient of static friction is \(\mu_{s}\). A projectile of mass \(m\) is fired frontally along the direction of the axis of the spring and hits with speed \(v\) the free end of the spring itself and compresses it. The device that fires the projectile can vary the initial speed. Determine the initial speed \(v^{*}\) beyond which the block will creep.

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