Part B

A spring is stretched $175$ mm by an $8-$ kg block. The block is displaced $100$ mm downward from its equilibrium position and given a downward velocity of $\backslash (1\mathrm{.}50\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Assume that positive displacement $\backslash ($ y $\backslash )$ is downward.

Determine the position of the block when $\backslash ($ t$=0\mathrm{.}27\backslash$mathrm$\{$~s$\}\backslash ).$

Express your answer to three significant figures and include the appropriate units.

View Available Hint$($s$)$

Hint $1.$ How to determine the position of the block

Apply the general solution of the differential equation. You can find the constants of integration using the block's position and velocity at $\backslash ($ t$=0\backslash ).$ The expression for velocity is determined by taking the time derivative of the general solution.

$\backslash [$

y$=\backslash$square $\backslash$mathrm$\{$m$\}$

$\backslash ]$