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A mass hanging from a spring is set in motion and its ensuing velocity is given by v$($t$)=4cost$ for $t0.$ Assume that the positive direction is upward and s$(0)=0.$

b$.$ Determine the position function for $t0.$

c$.$ At what times position function on the interval $0,3$

d$.$ At what times does the mass reach its lowest point the first three times?

$($hree times?

$s(t)=$

b$.$ Graph the position function on the interval $0,3.$ Choose the correct graph below.

c$.$ At what times does the mass reach its lowest point the first three times?

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$($Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.$)$ d$.$ At what times does the mass reach its highest point the first three times?

$($Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.$)$