A block of mass \(M\) is attached to an ideal horizontal spring of spring constant \(k\) and undergoes simple harmonic motion on a frictionless surface with amplitude \(A_0\) and frequency \(f_0\). A lump of sticky clay of mass \(m\) is dropped vertically from a negligible height onto the block and immediately sticks to it without slipping. In Scenario 1, the clay sticks to the block at the instant the block is at a turnaround point (\(x = A_0\)); in Scenario 2, an identical lump of clay sticks to the block at the instant the block passes through the equilibrium position (\(x = 0\)). Which of the following correctly expresses the resulting amplitude and frequency of oscillation for each scenario?