A mass m $=1\mathrm{.}1$ kg hangs at the end of a vertical spring whose top end is fixed to the celling. The spring has spring constant k $=105$ N$/$m and negligible mass. At time t $=0$ the mass is released from rest at a distance d $=\mathrm{.}45$ m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y$($t$)=$ Acos$($t $$ $).$ The positive y$-$axis points upward.

Find the angular frequency of oscillation, in radians per second.

Determine the magnitude of the coefficient A$,$ in meters.

Determine the value of $,$ in radians.

Enter an expression for the velocity along the y$-$axis as a function of time, in terms of A$,$ $,$ $,$ and t$.$

WHat is the magnitude of the mass's maximum acceleration, in meters per second squared?