Label: left parenthesis, 0 , 0 , right parenthesis0,0
Label:
7
Label: left parenthesis, 82.6 , negative 134.9 7 5 , right parenthesis82.6,−134.975
Label:
8
`v\left(t\right)=\sqrt{\frac{mg}{k}}\tanh\left(\operatorname{arctanh}\left(v_{0}\sqrt{\frac{k}{mg}}\right)-t\sqrt{\frac{kg}{m}}\right)\left\{t\ge0\right\}` left parenthesis, 48.7 , negative 83.2 , right parenthesis48.7,−83.2
Label:
9
10
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left parenthesis, 0 , 0 , right parenthesis0,0
left parenthesis, 82.6 , negative 134.9 7 5 , right parenthesis82.6,−134.975
"v" left parenthesis, "t" , right parenthesis equals StartRoot, StartFraction, "m" "g" Over "k" , EndFraction , EndRoot hyperbolic tangent left parenthesis, arctanh left parenthesis, "v" Subscript, 0 , Baseline StartRoot, StartFraction, "k" Over "m" "g" , EndFraction , EndRoot , right parenthesis minus "t" StartRoot, StartFraction, "k" "g" Over "m" , EndFraction , EndRoot , right parenthesis left brace, "t" greater than or equal to 0 , right bracevt=mgktanharctanhv0kmg−tkgmt≥0