A mass $m=1\mathrm{.}5kg$ hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant $k=125\frac{N}{m}$ and negligible mass. At time $t=0$ the mass is released from rest at a distance $d=0\mathrm{.}35m$ 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.

Part $($a$)$

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

$=$

Grade Summary

Deductions

Potential

$100\%$

$10$

Submissions $q,$

Attempt$($s$)$ Remaining: $66$ Free Attempt$($s$),$ then $\frac{?}{\text{b}\text{a}\text{r}}(0)\%$ Deduction per Attempt detailed view

Hint

$6$ Free Submission$($s$)$ Remaining

Hints: $0\%$ deduction per hint. Hints remaining: $1$ Feedback: $0\%{?}_{?}$ deduction per feedback.

Part $($b$)$

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

Part $($c$)$

Determine the value of $,$ in radians.

Part $($d$)$

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

Part $($e$)$

What is the mass's velocity, in meters per second, at time $t_1=0\mathrm{.}15s?$

Part $($f$)$

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