A $160$ g block hangs from a spring with spring constant $\backslash (16\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ At $\backslash ($ t$=0\backslash$mathrm$\{$~s$\}\backslash )$ the block is $19$ cm below the equilibrium point and moving upward with a speed of $\backslash (140\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$s$\}\backslash ).$

What is the block's distance from equilibrium when the speed is $\backslash (72\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$s$\}\backslash )?$

Express your answer with the appropriate units.

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Hint $1.$ Potential energy

Use the law of conservation of energy. It is more convenient to measure the distance from when determining potential energy. You do not have to consider the gravitational potential

Correct

Part C

What is the block's distance from equilibrium at $\backslash ($ t$=3\mathrm{.}0\backslash$mathrm$\{$~s$\}\backslash )?$

Express your answer with the appropriate units. Enter positive value if the block is above the $\backslash (\backslash$epsilon $\backslash )$ negative value if the block is below the equilibrium point.

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Hint $1.$ How to approach the problem

Determine the angular frequency, the amplitude, and the phase constant of the block's oscillation distance as a function of time.