A mass m $=1\mathrm{.}2$ kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k $=115$ N$/$m and negligible mass. At time t $=0$ the mass is released from rest at a distance d $=0\mathrm{.}45$ m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y$($t$)=$ A cos$($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.

A

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$.$

v$($t$)$

What is the mass$$s velocity, in meters per second, at time t$1=0\mathrm{.}25$ s$?$

v$($t$1)$

What is the magnitude of the mass$$s maximum acceleration, in meters per second squared?

ama