A spring hangs vertically from a bracket at its unweighted equilibrium length, as shown in the leftmost image. An object with mass $m$ is attached to the lower end of the spring, and it is gently lowered until the spring reaches its new equilibrium length, as shown in the center figure. Referring to the right$-$most figure, the mass is raised until the spring returns to its original length, and then it is released from rest resulting in vertical oscillations.

Part $($a$)$

If the spring constant is $12\frac{N}{m},$ and the mass of the object is $0\mathrm{.}25$ kg $,$ find the oscillation amplitude, in meters.

$A=,m$

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Part $($b$)$

Find the maximum velocity, in meters per second, of the oscillating mass.