(Solved): A mass hanging from a spring is set in motion and its ensuing velocity is given by \( v(t)=2 \pi \ ...

A mass hanging from a spring is set in motion and its ensuing velocity is given by \( v(t)=2 \pi \cos \pi t \) for \( t \geq 0 \). Assume that the positive direction is upward and \( s(0)=0 \). a. Determine the position function for \( t \geq 0 \). b. Graph the position function on the interval \( [0,3] \). c. At what times does the mass reach its lowest point the first three times? d. At what times does the mass reach its highest point the first three times? a. Determine the position function for \( t \geq 0 \). \( \mathrm{s}(\mathrm{t})= \) b. Graph the position function on the interval \( [0,3] \). Choose the correct graph below. A. B. C. D. c. At what times does the mass reach its lowest point the first three times? ( ¡implify 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.)